prasanna chandra financial management

7/27/2019 prasanna chandra financial management

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Chapter 7TIME VALUE OF MONEY

1. Value five years hence of a deposit of Rs.1,000 at various interest rates is as follows:

r = 8% FV5 = Rs.1!"

r = 10% FV5 = Rs.1!11

r = 1#% FV5 = Rs.1$!#

r = 15% FV5 = Rs.#011

#. 0 years

. &n 1# years Rs.1000 'rows to Rs.8000 or 8 ti(es. )his is #ti(es the initial deposit. *encedou+lin' taes place in 1# - = years.

ccordin' to the Rule of !", the dou+lin' period is:

0.5 / !" - &nterest rate

uatin' this to and solvin' for interest rate, we 'et

&nterest rate = 18."%.

. 2avin' Rs.#000 a year for 5 years and Rs.000 a year for 10 years thereafter is euivalent tosavin' Rs.#000 a year for 15 years and Rs.1000 a year for the years ! throu'h 15.*ence the savin's will cu(ulate to:#000 3 FV&F 410%, 15 years / 1000 3 FV&F 410%, 10 years= #000 3 1.$$# / 1000 3 15."$ = Rs.$"81.

5. 6et +e the annual savin's.

3 FV&F 41#%, 10 years = 1,000,000 3 1$.5" = 1,000,000

2o, = 1,000,000 - 1$.5" = Rs.5!,"8.

!. 1,000 3 FV&F 4r, ! years = 10,000

FV&F 4r, ! years = 10,000 - 1000 = 10

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Fro( the ta+les we find that

FV&F 4#0%, ! years = "."0FV&F 4#%, ! years = 10."80

7sin' linear interpolation in the interval, we 'et:

#0% / 410.000 "."0 r= 3 % = #0.% 410."80 "."0

$. 1,000 3 FV&F 4r, 10 years = 5,000FV&F 4r,10 years = 5,000 - 1000 = 5


FV&F 41!%, 10 years = .11FV&F 418%, 10 years = 5.#

7sin' linear interpolation in the interval, we 'et:

45.000 .11) 3 #% r= 1!% / = 1$.%

45.# .11

8. )he present value of Rs.10,000 receiva+le after 8 years for various discount rates 4r are:r= 10% 9V = 10,000 3 9V&F4r= 10%, 8 years

= 10,000 3 0.!$ = Rs.,!$0

r= 1#% 9V = 10,000 3 9V&F 4r= 1#%, 8 years= 10,000 3 0.0 = Rs.,00

r= 15% 9V = 10,000 3 9V&F 4r= 15%, 8 years= 10,000 3 0.#$ = Rs.,#$0

". ssu(in' that it is an ordinary annuity, the present value is:#,000 3 9V&F 410%, 5years= #,000 3 .$"1 = Rs.$,58#

10. )he present value of an annual pension of Rs.10,000 for 15 years whenr= 15% is:10,000 3 9V&F 415%, 15 years= 10,000 3 5.8$ = Rs.58,$0

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)he alternative is to receive a lu(psu( of Rs.50,000.

+viously, ;r.


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9V&F 41#%, years / Rs.500 3 9V&F 41#%, 5 years /Rs.!00 3 9V&F 41#%, ! years / Rs.$00 3 9V&F 41#%, $ years /

Rs.800 3 9V&F 41#%, 8 years / Rs."00 3 9V&F 41#%, " years /Rs.1,000 3 9V&F 41#%, 10 years

= Rs.100 3 0.8" / Rs.#00 3 0.$"$ / Rs.00 3 0.$1# / Rs.00 3 0.!! / Rs.500 3 0.5!$ / Rs.!00 3 0.50$

/ Rs.$00 3 0.5# / Rs.800 3 0.0 / Rs."00 3 0.!1 / Rs.1,000 3 0.##

= Rs.#5"0."

2i(ilarly,9V 42trea( > = Rs.,!#5.#9V 42trea( ? = Rs.#,851.1

1$. FV5 = Rs.10,000 @1 / 40.1! - A53

= Rs.10,000 41.0#0

= Rs.10,000 3 #.1"1

= Rs.#1,"10

18. FV5 = Rs.5,000 @1/4 0.1#-A53

= Rs.5,000 41.0#0

= Rs.5,000 3 1.80!= Rs.",00

1" A B C

2tated rate 4% 1# # #

Freuency of co(poundin' ! ti(es ti(es 1# ti(es

ffective rate 4% 41 / 0.1#-!! 1 41/0.#-1 41 / 0.#-1#1#1

= 1#.! = #!.# = #!.8

Bifference +etween theeffective rate and statedrate 4% 0.! #.# #.8

#0. &nvest(ent reuired at the end of 8th year to yield an inco(e of Rs.1#,000 per year fro( theend of "thyear 4+e'innin' of 10thyear for ever:

Rs.1#,000 3 9V&F41#%, C


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= Rs.1#,000 - 0.1# = Rs.100,000

)o have a su( of Rs.100,000 at the end of 8

th

year , the a(ount to +e deposited now is: Rs.100,000 Rs.100,000= = Rs.0,88

9V&F41#%, 8 years #.$!

#1. )he interest rate i(plicit in the offer of Rs.#0,000 after 10 years in lieu of Rs.5,000 now is:Rs.5,000 3 FV&F 4r,10 years = Rs.#0,000

Rs.#0,000FV&F 4r,10 years = = .000

Rs.5,000

Fro( the ta+les we find thatFV&F 415%, 10 years = .0!

)his (eans that the i(plied interest rate is nearly 15%.

& would choose Rs.#0,000 for 10 years fro( now +ecause & find a return of 15% uiteaccepta+le.

##. FV10 = Rs.10,000 @1 / 40.10 - #A103#

= Rs.10,000 41.05#0

= Rs.10,000 3 #.!5= Rs.#!,50

&f the inflation rate is 8% per year, the value of Rs.#!,50 10 years fro( now, in ter(s ofthe current rupees is:Rs.#!,50 3 9V&F 48%,10 years= Rs.#!,50 3 0.! = Rs.1#,#8

#. constant deposit at the +e'innin' of each year represents an annuity due.9V&F of an annuity due is eual to : 9V&F of an ordinary annuity 3 41 / r)o provide a su( of Rs.50,000 at the end of 10 years the annual deposit should

+e

Rs.50,000 = FV&F41#%, 10 years 3 41.1#

Rs.50,000= = Rs.#5

1$.5" 3 1.1#

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#. )he discounted value of Rs.#0,000 receiva+le at the +e'innin' of each year fro( #005 to#00", evaluated as at the +e'innin' of #00 4or end of #00 is:

Rs.#0,000 3 9V&F 41#%, 5 years= Rs.#0,000 3 .!05 = Rs.$#,100.

)he discounted value of Rs.$#,100 evaluated at the end of #000 isRs.$#,100 3 9V&F 41#%, years

= Rs.$#,100 3 0.$1# = Rs.51,5

&f is the a(ount deposited at the end of each year fro( 1""5 to #000 then 3 FV&F 41#%, ! years = Rs.51,5 3 8.115 = Rs.51,5 = Rs.51,5 - 8.115 = Rs.!#!

#5. )he discounted value of the annuity of Rs.#000 receiva+le for 0 years, evaluated as at theend of "thyear is:

Rs.#,000 3 9V&F 410%, 0 years = Rs.#,000 3 ".#$ = Rs.18,85)he present value of Rs.18,85 is:

Rs.18,85 3 9V&F 410%, " years

= Rs.18,85 3 0.#= Rs.$,""

#!. 0 per cent of the pension a(ount is0.0 3 Rs.!00 = Rs.180

ssu(in' that the (onthly interest rate correspondin' to an annual interest rate of 1#% is1%, the discounted value of an annuity of Rs.180 receiva+le at the end of each (onth for 180(onths 415 years is:

Rs.180 3 9V&F 41%, 180

41.01180 1Rs.180 3 = Rs.1,""8

.01 41.01180

&f ;r. Ra(esh +orrows Rs.Ptoday on which the (onthly interest rate is 1%

P 3 41.01!0 = Rs.1,""8P 3 1.81$ = Rs.1,""8

Rs.1,""8P = = Rs.8#5

1.81$

#$. Rs.00 3 9V&F4r, # (onths = Rs.!,0009V&F 4%,# = Rs.!000 - Rs.00 = #0

Fro( the ta+les we find that:

9V&F41%,# = #1.#

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9V&F 4#%, # = 18."1

7sin' a linear interpolation#1.# #0.000r = 1% / 3 1%

#1.# 18,"1

= 1.5%

)hus, the +an char'es an interest rate of 1.5% per (onth.)he correspondin' effective rate of interest per annu( is

@ 41.0151# 1 A 3 100 = #0%

#8. )he discounted value of the de+entures to +e redee(ed +etween 8 to 10 years evaluated atthe end of the 5thyear is:

Rs.10 (illion 3 9V&F 48%, years / Rs.10 (illion 3 9V&F 48%, years / Rs.10 (illion 3 9V&F 48%, 5 years

= Rs.10 (illion 40.$" / 0.$5 / 0.!81 = Rs.#.#1 (illion

&f is the annual deposit to +e (ade in the sinin' fund for the years 1 to 5,then 3 FV&F 48%, 5 years = Rs.#.#1 (illion 3 5.8!$ = Rs.#.#1 (illion = 5.8!$ = Rs.#.#1 (illion

= Rs.#.#1 (illion - 5.8!$ = Rs.0.$$ (illion

#". 6et DnE +e the nu(+er of years for which a su( of Rs.#0,000 can +e withdrawn annually.

Rs.#0,000 3 9V&F 410%, n = Rs.100,0009V&F 415%, n = Rs.100,000 - Rs.#0,000 = 5.000


9V&F 410%, $ years = .8!89V&F 410%, 8 years = 5.5

)hus n is +etween $ and 8. 7sin' a linear interpolation we 'et

5.000 .8!8n= $ / 3 1 = $. years

5.5 .8!8

$


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0. uated annual install(ent = 500000 - 9V&F41%,= 500000 - #."1= Rs.1$1,585

Loan Amortisation Schedule

Beginning Annual Principal Remaining

Year amount installment Interest repaid balance

------ ------------- --------------- ----------- ------------- -------------

1 500000 1$1585 $0000 101585 "815 # "815 1$1585 55$$8 11580$ #8#!08 #8#!08 1$1585 "5!5 1#0#0 150588 150588 1$1585 #108# 15050 85

4 roundin' off error

1. Befine nas the (aturity period of the loan. )he value of n can +e o+tained fro( the

euation.

#00,000 3 9V&F41%, n = 1,500,0009V&F 41%, n = $.500

Fro( the ta+les or otherwise it can +e verified that 9V&F41,0 = $.500*ence the (aturity period of the loan is 0 years.

#. 3pected value of iron ore (ined durin' year 1 = Rs.00 (illion

3pected present value of the iron ore that can +e (ined over the ne3t 15 years assu(in' aprice escalation of !% per annu( in the price per tonne of iron

1 41 /gn- 41 / in

= Rs.00 (illion 3 ig

= Rs.00 (illion 3 1 41.0!15 - 41.1!150.1! 0.0!

= Rs.00 (illion 3 40.$15 - 0.10

= Rs.### (illion

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MINICASE

Solution:

1. *ow (uch (oney would Ra(esh need 15 years fro( nowG

500,000 3 9V&F 410%, 15years/ 1,000,000 3 9V&F 410%, 15years= 500,000 3 $.!0! / 1,000,000 3 0.#"= ,80,000 3 #",000= Rs.,0#,000

#. *ow (uch (oney should Ra(esh save each year for the ne3t 15 years to +e a+le to (eet hisinvest(ent o+HectiveG

Ra(eshEs current capital of Rs.!00,000 will 'row to :

!00,000 41.1015= !00,000 3 .1$$ = Rs #,50!,#00

)his (eans that his savin's in the ne3t 15 years (ust 'row to :

,0#,000 #,50!,#00 = Rs 1,55,800

2o, the annual savin's (ust +e : 1,55,800 1,55,800

= = Rs.8,8

FV&F 410%, 15 years 1.$$#

. *ow (uch (oney would Ra(esh need when he reaches the a'e of !0 to (eet his donationo+HectiveG

#00,000 3 9V&F 410% , yrs 3 9V&F 410%, 11yrs

= #00,000 3 #.8$ 3 0.1$ = 15$,!$!

. Ihat is the present value of Ra(eshEs life ti(e earnin'sG

00,000 00,00041.1# 00,00041.1#1

! 1 # 15

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1.1# 15

1 1.08

= 00,0000.08 0.1#

= Rs.$,#5,"!#

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Chapter 8

VALUATION OF BONS AN STOC!S

1. 5 11 100

P = /t=1 41.15 41.155

= Rs.11 3 9V&F415%, 5 years / Rs.100 3 9V&F 415%, 5 years= Rs.11 3 .5# / Rs.100 3 0."$= Rs.8!.$

#.4i Ihen the discount rate is 1%$ 1# 100

P = /t=1 41.1t 41.1$

= Rs.1# 3 9V&F 41%, $ years / Rs.100 3 9V&F 41%, $ years= Rs.1# 3 .#88 / Rs.100 3 0.= Rs."1.!

4ii Ihen the discount rate is 1#%$ 1# 100

P = / = Rs.100t=1 41.1#t 41.1#$

Jote that when the discount rate and the coupon rate are the sa(e the value is eual topar value.

. )he yield to (aturity is the value of r that satisfies the followin' euality. $ 1#0 1,000

Rs.$50 = / = Rs.100 t=1 41/rt 41/r$

)ry r = 18%. )he ri'ht hand side 4R*2 of the a+ove euation is:Rs.1#0 3 9V&F 418%, $ years / Rs.1,000 3 9V&F 418%, $ years= Rs.1#0 3 .81# / Rs.1,000 3 0.1= Rs.$$1.

)ry r= #0%. )he ri'ht hand side 4R*2 of the a+ove euation is:Rs.1#0 3 9V&F 4#0%, $ years / Rs.1,000 3 9V&F 4#0%, $ years= Rs.1#0 3 .!05 / Rs.1,000 3 0.#$"= Rs.$11.!0

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)hus the value of rat which the R*2 +eco(es eual to Rs.$50 lies +etween 18% and #0%.7sin' linear interpolation in this ran'e, we 'et

$$1. $50.00Kield to (aturity = 18% / $$1. $11.!0 3 #%

= 18.$%.

10 1 100

80 = /t=1 41/rt 41/r10

)ry r= 18%. )he R*2 of the a+ove euation is

Rs.1 3 9V&F 418%, 10 years / Rs.100 3 9V&F 418%, 10 years= Rs.1 3 ." / Rs.100 3 0.1"1 = Rs.8#

)ry r = #0%. )he R*2 of the a+ove euation is

Rs.1 3 9V&F4#0%, 10 years / Rs.100 3 9V&F 4#0%, 10 years= Rs.1 3 .1" / Rs.100 3 0.1!#= Rs.$."

7sin' interpolation in the ran'e 18% and #0% we 'et:

8# 80Kield to (aturity = 18% / 3 #%

8# $."

= 18.5!%

5.1# ! 100

P = /t=1 41.08t 41.081#

= Rs.! 3 9V&F 48%, 1# years / Rs.100 3 9V&F 48%, 1# years= Rs.! 3 $.5! / Rs.100 3 0."$= Rs.8."#

!. )he postta3 interest and (aturity value are calculated +elow:

1#


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Bond A Bond B

9ostta3 interest 4? 1#41 0. 10 41 0.=Rs.8. =Rs.$

9ostta3 (aturity value 4; 100 100 @ 4100$03 0.1A @ 4100 !03 0.1A=Rs."$ =Rs."!

)he postta3 K);, usin' the appro3i(ate K); for(ula is calculated +elow

8. / 4"$$0-10>ond : 9ostta3 K); =

0.! 3 $0 / 0. 3 "$

= 1.$%

$ / 4"! !0-!>ond > : 9ostta3 K); =

0.!3 !0 / 0. 3 "!

= 1$. $%

$.1 ! 100

P = /t=1 41.08t 41.081

= Rs.! 3 9V&F48%, 1 / Rs.100 3 9V&F 48%, 1= Rs.! 3 8.# / Rs.100 3 0.1= Rs.8.5!

8. Do = Rs.#.00,g= 0.0!, r = 0.1#

Po = D1- 4rg = Do41 /g - 4rg

= Rs.#.00 41.0! - 40.1# 0.0!= Rs.5.

2ince the 'rowth rate of !% applies to dividends as well as (aret price, the (aretprice at the end of the #ndyear will +e:

P# = Po3 41 /g#= Rs.5. 41.0!#

= Rs.".$0

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". Po = D1- 4rg = Do41 /g - 4rg= Rs.1#.00 41.10 - 40.15 0.10 = Rs.#!

10. Po = D1- 4rg

Rs.# = Rs.# - 0.1# gg = 0.05$5 or 5.$5%

11. Po = D1- 4rg = Do41/g - 4rgDo = Rs.1.50, g = 0.0, Po = Rs.8

2o8 = 1.50 41 .0 - 4r4.0 = 1. - 4r/ .0

*ence r = 0.1 or 1 per cent

1#. )he (aret price per share of ?o((onwealth ?orporation will +e the su( of threeco(ponents:

: 9resent value of the dividend strea( for the first years>: 9resent value of the dividend strea( for the ne3t years?: 9resent value of the (aret price e3pected at the end of 8 years.

= 1.50 41.1# - 41.1 / 1.50 41.1##- 41.1#/ 1.5041.1#- 41.1// 1.50 41.1#- 41.1

= 1.!8-41.1 / 1.88 - 41.1# / #.11 - 41.1 / #.! - 41.1

= Rs.5.$

> = #.!41.08 - 41.15/ #.! 41.08#- 41.1!/ #.! 41.08- 41.1$ // #.! 41.08- 41.18

= #.55 - 41.15/ #.$5 - 41.1!/ #."$ - 41.1$ / .#1 - 41.18

= Rs..8"

? = P8- 41.18

P8=D"- 4rg = .#1 41.05- 40.1 0.05 = Rs.$.52o

? = Rs.$.5 - 41.18 = Rs.1.1

)hus,

Po = / > / ? = 5.$ / .8" / 1.1

1


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= Rs.#.$$

1. )he intrinsic value of the euity share will +e the su( of three co(ponents:

: 9resent value of the dividend strea( for the first 5 years when the'rowth rate e3pected is 15%.

>: 9resent value of the dividend strea( for the ne3t 5 years when the'rowth rate is e3pected to +e 10%.

?: 9resent value of the (aret price e3pected at the end of 10 years.

#.00 41.15 #.00 41.15# #.00 41.15 #.0041.15 #.00 41.155

= / / / / 41.1# 41.1## 41.1.# 41.1.# 41.1#5

= #.0 - 41.1# / #.!5 - 41.1## / .0 - 41.1#/ .50 - 41.1# / .0#-41.1#5

= Rs.10.8

.0#41.10 .0# 41.10# .0#41.10 .0#41.10 .0# 41.105

> = / / / / 41.1#! 41.1#$ 41.1#8 41..1#"41.1#10 .# .8! 5.5 5.8" !.8

= / / / / 41.1#! 41.1#$ 41.1#8 41.1.#"41.1#10

= Rs.10.81

B11 1 !.8 41.05? = 3 = 3 1-41.1#10

rg 41 /r10 0.1# 0.05

= Rs."$.#0

)he intrinsic value of the share = / > / ?

= 10.8 / 10.81 / "$.#0 = Rs.118.85

1. )er(inal value of the interest proceeds= 10 3 FV&F 41!%,= 10 3 5.0!!= $0".#

Rede(ption value = 1,000

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)er(inal value of the proceeds fro( the +ond = 1$0".#

Befine r as the yield to (aturity. )he value of r can +e o+tained fro( the euation

"00 41 / r = 1$0".#r = 0.1$" or 1$."%

15. &ntrinsic value of the euity share 4usin' the #sta'e 'rowth (odel

41.18!

#.! 3 1 #.! 3 41.1853 41.1#

41.1!!

= / 0.1! 0.18 40.1! 0.1# 3 41.1!!

0.10801= #.! 3 / !#.05

0.0#

= Rs.$.80

1!. &ntrinsic value of the euity share 4usin' the * (odel

.00 41.#0 .00 3 3 40.10= /

0.18 0.10 0.18 0.10

= !0 / #0= Rs.80

1!


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Chapter "

#IS! AN #ETU#N

1 4a 3pected price per share a year hence will +e:

= 0. 3 Rs.10 / 0. 3 Rs.11 / 0.# 3 Rs.1# = Rs.10.80

4+ 9ro+a+ility distri+ution of the rate of return is

Rate of return 4Ri 10% #0% 0%

9ro+a+ility 4pi 0. 0. 0.#

Jote that the rate of return is defined as:

Bividend / )er(inal price 1

&nitial price

4c )he standard deviation of rate of return is : L = pi4RiR#

)he L of the rate of return on ;V;Es stoc is calculated +elow:Ri pi pI ri 4Ri-R 4Ri- R

# pi4Ri-R#

10 0. 8 ! #5.!#0 0. 8 # 1.!

0 0.# ! 1# 1 #8.8

R= piRi pi4Ri-R#

= 5!

L = 5! = $.8%

# 4a For Rs.1,000, #0 shares of lphaEs stoc can +e acuired. )he pro+a+ility distri+ution of thereturn on #0 shares is

Economic Condition Return4Rs Probability*i'h Mrowth #0 3 55 = 1,100 0.6ow Mrowth #0 3 50 = 1,000 0.2ta'nation #0 3 !0 = 1,#00 0.#Recession #0 3 $0 = 1,00 0.#

3pected return = 41,100 3 0. / 41,000 3 0. / 41,#00 3 0.# / 41,00 3 0.#

1$


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= 0 / 00 / #0 / #80= Rs.1,150

2tandard deviation of the return = @41,100 1,150#3 0. / 41,000 1,150# 3

0. / 41,#00 1,150# 3 0.# / 41,00 1,150# 3 0.#A1-#

= Rs.1.18

4+ For Rs.1,000, #0 shares of >etaEs stoc can +e acuired. )he pro+a+ility distri+ution of thereturn on #0 shares is:

Economic condition Return Rs! Probability

*i'h 'rowth #0 3 $5 = 1,500 0.6ow 'rowth #0 3 !5 = 1,00 0.2ta'nation #0 3 50 = 1,000 0.#Recession #0 3 0 = 800 0.#

3pected return = 41,500 3 0. / 41,00 3 0. / 41,000 3 0.# / 4800 3 0.#= Rs.1,#00

2tandard deviation of the return = @41,500 1,#00#3 . / 41,00 1,#00#3 ./ 41,000 1,#00#3 .# / 4800 1,#00# 3 .#A1-# = Rs.#!.58

4c For Rs.500, 10 shares of lphaEs stoc can +e acuiredN liewise for Rs.500, 10shares of >etaEs stoc can +e acuired. )he pro+a+ility distri+ution of this option is:

Return Rs! Probability410 3 55 / 410 3 $5 = 1,00 0.410 3 50 / 410 3 !5 = 1,150 0.410 3 !0 / 410 3 50 = 1,100 0.#410 3 $0 / 410 3 0 = 1,100 0.#

3pected return = 41,00 3 0. / 41,150 3 0. / 41,100 3 0.# /41,100 3 0.#

= Rs.1,1$52tandard deviation = @41,00 1,1$5#3 0. / 41,150 1,1$5#3 0. /

41,100 1,1$5#3 0.# / 41,100 1,1$5#3 0.# A1-#

= Rs.8.1d. For Rs.$00, 1 shares of lphaEs stoc can +e acuiredN liewise for Rs.00, !

shares of >etaEs stoc can +e acuired. )he pro+a+ility distri+ution of thisoption is:

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Return Rs! Probability

41 3 55 / 4! 3 $5 = 1,##0 0.41 3 50 / 4! 3 !5 = 1,0"0 0.41 3 !0 / 4! 3 50 = 1,10 0.#41 3 $0 / 4! 3 0 = 1,##0 0.#

3pected return = 41,##0 3 0. / 41,0"0 3 0. / 41,10 3 0.# / 41,##0 3 0.#= Rs.1,1!5

2tandard deviation = @41,##0 1,1!5#3 0. / 41,0"0 1,1!5# 3 0. /41,10 1,1!5#3 0.# / 41,##0 1,1!5#3 0.#A1-#

= Rs.5$.!!

)he e3pected return to standard deviation of various options are as follows :

"ption

E#pected return

Rs!

Standard de$iation

RsE#pected % Standard

return de$iation

a 1,150 1 8.0

+ 1,#00 #!5 .5c 1,1$5 8 1.""

d 1,1!5 58 #0.0"

ption DdE is the (ost preferred option +ecause it has the hi'hest return to ris ratio.

. 3pected rates of returns on euity stoc , >, ? and B can +e co(puted as follows:

: 0.10 / 0.1# / 40.08 / 0.15 / 40.0# / 0.#0 = 0.0$8 = $.8%!

>: 0.08 / 0.0 / 0.15 /.1# / 0.10 / 0.0! = 0.0"1$ = ".1$%!

?: 0.0$ / 0.08 / 0.1# / 0.0" / 0.0! / 0.1# = 0.0"00 = ".00%!

B: 0.0" / 0.0" / 0.11 / 0.0 / 0.08 / 0.1! = 0.0"5 = ".50%!

4a Return on portfolio consistin' of stoc = $.8%

4+ Return on portfolio consistin' of stoc and > in eualproportions = 0.5 40.0$8 / 0.5 40.0"1$

= 0.085 = 8.5%

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4c Return on portfolio consistin' of stocs , > and ? in eualproportions = 1-40.0$8 / 1-40.0"1$ / 1- 40.0"0

= 0.08!$ = 8.!$%

4d Return on portfolio consistin' of stocs , >, ? and B in eualproportions = 0.#540.0$8 / 0.#540.0"1$ / 0.#540.0"00 /

0.#540.0"5= 0.088$5 = 8.88%

. BefineRAandR&as the returns on the euity stoc of uto lectricals 6i(ited a and ;aret

portfolio respectively. )he calculations relevant for calculatin' the +eta of the stoc areshown +elow:

Year RA R& RA-RA R&-R& RA-RA! R&-R&! RA-RA%R&-R&1 15 1# 0.0" .18 0.01 10.11 0.#"

# ! 1 #1.0" 1.18 .$" #01.0$ #"".0!

18 1 #."1 1.18 8.$ 1." .

0 # 1."1 8.8# ###.1 $$.$" 11.51

5 1# 1! 0.0" 0.8# ".55 0.!$ #.5! #5 0 "."1 1.8# "8.#1 #1".! 1!.8$

$ # 1.0" 18.18 1$1.5 0.51 #$."8

8 #0 # ."1 8.8# #.11 $$.$" .1

" 18 15 #."1 0.18 8.$ 0.0 0.5#

10 # ## 8."1 !.8# $"." !.51 !0.$$

11 8. 1# $.0" .18 50.#$ 10.11 ##.55

RA= 15.0" R&= 15.18

4RARA#= 111!." 4R&R= "$5.!1 4RARA 4R&R& = "5.8!

>eta of the euity stoc of uto lectricals

4RARA 4R&R&

4R&R

= "5.8! = 0."!"$5.!1

lpha = RA OR&

= 15.0" 40."! 3 15.18= 0.5#

#0


21/164

uation of the characteristic line is

RA= 0.5# / 0."!R&

5. )he reuired rate of return on stoc is:

RA = R'/ OA4R&R'= 0.10 / 1.5 40.15 0.10= 0.1$5

&ntrinsic value of share =D1- 4rg =Do41/g - 4 rg

MivenDo= Rs.#.00,g= 0.08, r= 0.1$5 #.00 41.08

&ntrinsic value per share of stoc = 0.1$5 0.08

= Rs.##.$

!. )he 2;6 euation isRA=R'/ OA4R&R'

MivenRA= 15%. R'= 8%,R&= 1#%, we have

0.15 = .08 / OA40.1# 0.08

0.0$

i.e.OA = = 1.$5 0.0

>eta of stoc = 1.$5

$. )he 2;6 euation is: R(=R'/ O(4R&R'

Ie are 'iven 0.15 = 0.0" / 1.5 4R& 0.0" i.e., 1.5R&= 0.1"5

orR&= 0.1%

)herefore return on (aret portfolio = 1%

8. R&= 1#% O(= #.0 R(=18% g= 5% Po= Rs.0

Po =D1 - 4rg

Rs.0 =D1- 40.18 .05

#1


22/164

2oD1 = Rs." and Do =D1- 41/g = ." -41.05 = Rs..$1

R# = R)/ O#4R&R)

0.18 = R)/ #.0 40.1# R)

2oR)= 0.0! or !%.

"riginal Re$ised

R) !% 8%R&R) !% %g 5% %O# #.0 1.8

RevisedR#= 8% / 1.8 4% = 15.#%

9rice per share of stoc P, 'iven the a+ove chan'es is

.$1 41.0= Rs..5

0.15# 0.0

Chapter $%

O&TIONS AN T'EI# VALUATION

##


23/164

1. S= 100 u= 1.5 d= 0.8

E= 105 r= 0.1# R= 1.1#

)he values of 4hed'e ratio andB4a(ount +orrowed can +e o+tained as follows:

Cu CdQ =

4u d S

Cu = ;a3 4150 105, 0 = 5

Cd = ;a3 480 105, 0 = 0

5 0 5 "Q = = = = 0.!#"

0.$ 3 100 $0 1

u.Cd d.Cu

B =4udR

41.5 3 0 40.8 3 5=

0.$ 3 1.1#

!

= = 5."#0.$8

C = Q S/B= 0.!#" 3 100 5."#= Rs.18.$

Value of the call option = Rs.18.$

#. S= 0 u= G d= 0.8R= 1.10 E= 5 C= 8

Ie will assu(e that the current (aret price of the call is eual to the pair value of the callas per the >ino(ial (odel.

Miven the a+ove data

#


24/164

Cd = ;a3 4# 5, 0 = 0

Q CuCd R= 3

B u Cd d Cu S

Q Cu 0 1.10= 3

B 0.8Cu 0

= 4 0.0$5

Q = 0.$5B 41C = Q S/B8 = Q 3 0 / B 4#

2u+stitutin' 41 in 4# we 'et

8 = 40.0!5 3 0B/B

8 = 0.$5BorB = #1.

Q = 0.0$5 4#1. = 0.$#

)he portfolio consists of 0.$# of a share plus a +orrowin' of Rs.#1. 4entailin' arepay(ent of Rs.#1. 41.10 = Rs.#.! after one year. &t follows that whenuoccurs either u3 03 0.$# #.! = u3 0 5

10.!$# u = #1.5 u = #.0#

or

u3 0 3 0.$# #.! = 0u = 0.8

2ince u d, it follows that u= #.0#.9ut differently the stoc price is e3pected to rise +y 1.0# 3 100 = 10#%.

. 7sin' the standard notations of the >lac2choles (odel we 'et the followin' results:ln4S-E / rt/ L

#t-#

d1 =

#


25/164

t

= ln41#0 - 110 / 0.1 / 0.#-#

0.

= 0.08$01 / 0.1 / 0.08 0.

= 0.$!$5

d# = d1 t= 0.$!$5 0.= 0.!$5

*4d1 = *40.$!$5 S*40.$$ = 0.80$85*4d# = *40.!$5 S*40.$ = 0.!1

C = 2o*4d1 E. ert. *4d#

= 1#0 3 0.80$85 110 3 e0.13 0.!1

= 41#0 3 0.80$85 4110 3 0.8!"! 3 0.!1= 5.

Value of the call as per the >lac and 2choles (odel is Rs.5..

. t = 0.# 3 1 = 0.#

Ratio of the stoc price to the present value of the e3ercise price

80=

8# 3 9V&F 415.0,1

80=

8# 3 0.8!"= 1.1##

Fro( ta+le ! we find the percenta'e relationship +etween the value of the call option andstoc price to +e 1.1 per cent. *ence the value of the call option is

0.11 3 80 = Rs.11,#8.

5. Value of put option= Value of the call option/ 9resent value of the e3ercise price

#5


26/164

2toc price TTT 4

)he value of the call option 'ives an e3ercise price of Rs.85 can +e o+tained as follows:

t = 0.# 1 = 0.#

Ratio of the stoc price to the present value of the e3ercise price

80=

85 3 9V&F 415.0,1

= 80 - $.8" = 1.08

Fro( )a+le .!, we find the percenta'e relationship +etween the value of the call option andthe stoc price to +e 11."%

*ence the value of the call option = 0.11" 3 80 = Rs.".5#

9lu''in' in this value and the other relevant values in 4, we 'et

Value of put option = ".5# / 85 3 41.1501 80

= Rs..1

!. So = +o*4d1 B1ert*4d#

= !000*4d1 5000 e 0.1*4d#

ln4!000 - 5000 / 40.1 3 1 / 40.18-#d1 =

0.18 3 1

ln41.# / 0.1"=

0.#

= 0.8$$5 = 0.88

*4d1 = *40.88 = 0.8105$d# = d1 t

= 0.8$$5 0.18

#!


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= 0.5# = 0.5

*4d# = *40.5 = 0.!$!2o = !000 3 0.8105$ 45000 3 0."08 3 0.!$!

= 181!

B0 = +0 S0= !0000 181!= 18

Chapter $$

TEC'NI(UES OF CA&ITAL BUETIN

1.4a J9V of the proHect at a discount rate of 1%.

= 1,000,000 / 100,000 / #00,000 41.1 41.1#

/ 00,000 / !00,000 / 00,000

#$


28/164

41.1 41.1 41.15

= 8$

4+ J9V of the proHect at ti(e varyin' discount rates

= 1,000,000

/ 100,000

41.1#

/ #00,000

41.1# 41.1

/ 00,000

41.1# 41.1 41.1

/ !00,000

41.1# 41.1 41.1 41.15

/ 00,000

41.1# 41.1 41.141.1541.1!

= 1,000,000 / 8"#8! / 1580#8 / #0$"1 / !1!#0 / 1558$1= #$#!

#. &nvest(ent

a 9ay+ac period = 5 years+ J9V = 0000 3 9V&F 41#,10 #00 000

= #!000c &RR 4r can +e o+tained +y solvin' the euation:

0000 3 9V&F 4r, 10 = #00000i.e., 9V&F 4r, 10 = 5.000

Fro( the 9V&F ta+les we find that

#8


29/164

9V&F 415,10 = 5.01"9V&F 41!,10 = .88

6inear interporation in this ran'e yieldsr = 15 / 1 3 40.01" - 0.1! = 15.1%

d >?R = >enefit ?ost Ratio= 9V> - &= ##!,000 - #00,000 = 1.1

&nvest(ent >

a 9ay+ac period = " years

+ J9 V = 0,000 3 9V&F 41#,5/ 0,000 3 9V&F 41#,# 3 9V&F 41#,5/ #0,000 3 9V&F 41#, 3 9V&F 41#,$

- 00,000

= 40,000 3 .!05 / 40,000 3 1.!"0 3 0.5!$/ 4#0,000 3 #.0# 3 0.5# 00,000

= 105"

c &RR 4r can +e o+tained +y solvin' the euation0,000 3 9V&F 4r, 5 / 0,000 3 9V&F 4r, # 3 9V&F 4r,5 /#0,000 3 9V&F 4r, 3 9V&F 4r, $ = 00,000

)hrou'h the process of trial and error we find thatr= 1.$%

d >?R = 9V> - &= 1",!!1 - 00,000 = 0.!5

&nvest(ent ?

a 9ay+ac period lies +etween # years and years. 6inear interpolation in thisran'e provides an appro3i(ate pay+ac period of #.88 years.

+ J9V = 80.000 3 9V&F 41#,1 / !0,000 3 9V&F 41#,#/ 80,000 3 9V&F 41#, / !0,000 3 9V&F 41#,

/ 80,000 3 9V&F 41#,5 / !0,000 3 9V&F 41#,!

/ 0,000 3 9V&F 41#, 3 9V&F 41#.!

#"


30/164

#10,000= 111,$1

c &RR 4r is o+tained +y solvin' the euation

80,000 3 9V&F 4r,1 / !0,000 3 9V&F 4r,# / 80,000 3 9V&F 4r,/ !0,000 3 9V&F 4r, / 80,000 3 9V&F 4r,5 / !0,000 3 9V&F 4r,!/ 0000 3 9V&F 4r, 3 9V&F 4r,! = #10000

)hrou'h the process of trial and error we 'etr= #".#"%

d >?R = 9V> - & = #1,$1 - #10,000 = 1.5

&nvest(ent B

a 9ay+ac period lies +etween 8 years and " years. linear interpolation in thisran'e provides an appro3i(ate pay+ac period of 8.5 years.

8 / 41 3 100,000 - #00,000

+ J9V = #00,000 3 9V&F 41#,1/ #0,000 3 9V&F 41#,# / #00,000 3 9V&F 41#,"/ 50,000 3 9V&F 41#,10 #0,000

= $,1!0

c &RR 4r can +e o+tained +y solvin' the euation#00,000 3 9V&F 4r,1 / #00,000 3 9V&F 4r,#

/ #00,000 3 9V&F 4r," / 50,000 3 9V&F 4r,10= #0000

)hrou'h the process of trial and error we 'et r= 8.5%

d >?R = 9V> - & = #8#,80 - #0,000 = 0.88

?o(parative )a+le

In$estment A B C D

a 9ay+ac period4in years 5 " #.88 8.5

+ J9V U 1#% pa #!000 105" 111$1 $1!0

c &RR 4% 15.1 1.$ #".#" 8.5

0


31/164

d >?R 1.1 0.!5 1.5 0.88

(on' the four alternative invest(ents, the invest(ent to +e chosen is ?E+ecause it has the 6owest pay+ac period

*i'hest J9V*i'hest &RR*i'hest >?R

. &RR 4r can +e calculated +y solvin' the followin' euations for the value of r.!0000 3 9V&F 4r,$ = 00,000

i.e., 9V&F 4r,$ = 5.000

)hrou'h a process of trial and error it can +e verified that r= ".#0% pa.

. )he &RR 4r for the 'iven cashflow strea( can +e o+tained +y solvin' the followin' euationfor the value of r.

000 / "000 - 41/r 000 - 41/r = 0

2i(plifyin' the a+ove euation we 'et

r = 1.!1, 0.!1N 4or 1!1%, 4!1%

*",E: Miven two chan'es in the si'ns of cashflow, we 'et two values for the&RR of the cashflow strea(. &n such cases, the &RR rule +reas down.

5. Befine J?F as the (ini(u( constant annual net cashflow that Hustifies the purchase of the'iven euip(ent. )he value of J?F can +e o+tained fro( the euation

J?F 3 9V&F 410,8 = 500000J?F = 500000 - 5.5

= "#$1

!. BefineIas the initial invest(ent that is Hustified in relation to a net annual cash

inflow of #5000 for 10 years at a discount rate of 1#% per annu(. )he valueofIcan +e o+tained fro( the followin' euation

#5000 3 9V&F 41#,10 = Ii.e.,I = 11#5!

$. 9V of +enefits 49V> = #5000 3 9V&F 415,1/ 0000 3 9V&F 415,#/ 50000 3 9V&F 415,

1


32/164

/ 0000 3 9V&F 415,/ 0000 3 9V&F 415,5= 1##!! 4

&nvest(ent = 100,000 4>

>enefit cost ratio = 1.# @= 4 - 4>A

8. )he J9VEs of the three proHects are as follows:

&ro*e+t

P R

Discount rate

0% 00 500 !005% ## #51 1#

10% !" 0 $0

15% !! 1# 15

#5% #"1 5 !10% 8! 555 5"1

". J9V profiles for 9roHects 9 and W for selected discount rates are as follows:4a

&ro*e+t

P Discount rate .!

0 #"50 500 5 18$! #0810 10$5 #815 $1 ####0 11 8#

+ 4i )he &RR 4r of proHectPcan +e o+tained +y solvin' the followin'

euation for DrE.

1000 1#00 3 9V&F 4r,1 !00 3 9V&F 4r,# #50 3 9V&F 4r,/ #000 3 9V&F 4r, / 000 3 9V&F 4r,5 = 0

)hrou'h a process of trial and error we find that r = #0.1%

4ii )he &RR 4r' of proHect can +e o+tained +y solvin' the followin' euation for r'

#


33/164

1!00 / #00 3 9V&F 4r',1 / 00 3 9V&F 4r',# / !00 3 9V&F 4r',/ 800 3 9V&F 4r', / 100 3 9V&F 4r',5 = 0

)hrou'h a process of trial and error we find that r'= ".%.

c Fro( 4a we find that at a cost of capital of 10%

J9V 49 = 10$5J9V 4W = #8

Miven that J9V 49 . J9V 4WN and J9V 49 0, & would choose proHect 9.

Fro( 4a we find that at a cost of capital of #0%

J9V 49 = 11

J9V 4W = 8#

'ain J9V 49 J9V 4WN and J9V 49 0. & would choose proHect 9.

d 9roHect 9

9V of invest(entrelated costs

= 1000 3 9V&F 41#,0/ 1#00 3 9V&F 41#,1 / !00 3 9V&F 41#,#/ #50 3 9V&F 41#,

= #$#8)V of cash inflows = #000 3 41.1# / 000 = !#0)he ;&RR of the proHect 9 is 'iven +y the euation:

#$#8 = !#0 3 9V&F 4;&RR,541 / ;&RR5 = #.#8$;&RR = 18%

4c 9roHect W

9V of invest(entrelated costs = 1!00

)V of cash inflows U 15% p.a. = #$$#

)he ;&RR of proHect W is 'iven +y the euation:

1!000 41 / ;&RR5 = #$$#


34/164

;&RR = 11.!#%

10

4a 9roHect

J9V at a cost of capital of 1#%= 100 / #5 3 9V&F 41#,!= Rs.#.$" (illion

&RR 4r can +e o+tained +y solvin' the followin' euation for r.#5 3 9V&F 4r,! = 100

i.e., r= 1#,"8%

9roHect >

J9V at a cost of capital of 1#%, - 50 / 1 3 9V&F 41#,!

= Rs..5 (illion

&RR 4r' can +e o+tained +y solvin' the euation1 3 9V&F 4r',! = 50i.e., r'= 1.0% @deter(ined throu'h a process of trial and errorA

4+ Bifference in capital outlays +etween proHects and > is Rs.50 (illionBifference in net annual cash flow +etween proHects and > is Rs.1# (illion.

J9V of the differential proHect at 1#%= 50 / 1# 3 9V&F 41#,!= Rs..15 (illion

&RR 4r'' of the differential proHect can +e o+tained fro( the euation1# 3 9V&F 4r'', ! = 50i.e., r'' = 11.5%

114a 9roHect ;

)he pay +ac period of the proHect lies +etween # and years. &nterpolatin' inthis ran'e we 'et an appro3i(ate pay +ac period of #.! years-

9roHect J)he pay +ac period lies +etween 1 and # years. &nterpolatin' in this ran'e we'et an appro3i(ate pay +ac period of 1.55 years.


35/164

4+ 9roHect ;?ost of capital = 1#% p.a

9V of cash flows up to the end of year # = #."$9V of cash flows up to the end of year = $.$59V of cash flows up to the end of year = $1.#!

Biscounted pay +ac period 4B9> lies +etween and years. &nterpolatin' in this ran'e we'et an appro3i(ate B9> of .1 years.

9roHect J

?ost of capital = 1#% per annu(9V of cash flows up to the end of year 1 = ."9V of cash flows up to the end of year # = 51.$

B9> lies +etween 1 and # years. &nterpolatin' in this ran'e we 'et an appro3i(ateB9> of 1."# years.

4c 9roHect ;

?ost of capital = 1#% per annu(J9V = 50 / 11 3 9V&F 41#,1

/ 1" 3 9V&F 41#,# / # 3 9V&F 41#,/ $ 3 9V&F 41#,

= Rs.#1.#! (illion

9roHect J?ost of capital = 1#% per annu(

J9V = Rs.#0.! (illion2ince the two proHects are independent and the J9V of each proHect is 4/ ve,+oth the proHects can +e accepted. )his assu(es that there is no capital constraint.

4d 9roHect ;?ost of capital = 10% per annu(J9V = Rs.#5.0# (illion

9roHect J

?ost of capital = 10% per annu(J9V = Rs.#.08 (illion

2ince the two proHects are (utually e3clusive, we need to choose the proHect with the hi'herJ9V i.e., choose proHect ;.*",E: )he ;&RR can also +e used as a criterion of (erit for choosin' +etween the twoproHects +ecause their initial outlays are eual.

4e 9roHect ;?ost of capital = 15% per annu(

5


36/164

J9V = 1!.1 (illion

9roHect J

?ost of capital: 15% per annu(J9V = Rs.1$.# (illion'ain the two proHects are (utually e3clusive. 2o we choose the proHect with thehi'her J9V, i.e., choose proHect J.

4f 9roHect ;)er(inal value of the cash inflows: 11.$;&RR of the proHect is 'iven +y the euation

50 41 / ;&RR = 11.$i.e., ;&RR = #.01%

9roHect J)er(inal value of the cash inflows: 115.1;&RR of the proHect is 'iven +y the euation

50 4 1/ ;&RR = 115.1i.e., ;&RR = #.#!%

!


37/164

Chapter $.

ESTIMATION OF O/ECT CAS' FLO0S1.4a Pro/ect Cash 'lo0s Rs1 in million!

Year 2 3 4 5 6 7 8 9

1. 9lant X (achinery 4150

#. Iorin' capital 450

. Revenues #50 #50 #50 #50 #50 #50 #50

. ?osts 4e3cludin' de preciation X interest 100 100 100 100 100 100 100

5. Bepreciation $.5 #8.1 #1.0" 15.8# 11.8$ 8."0 !.!$

!. 9rofit +efore ta3 11#.5 1#1.8$ 1#8."1 1.18 18.1 11.11.

$. )a3 .$5 !.5! 8.!$ 0.#5 1. #. .0

8. 9rofit after ta3 $8.$5 85.1 "0.# "." "!.!" "8.$$100.

". Jet salva'e value of

plant X (achinery 8

10. Recovery of worin' 50 capital

11. &nitial outlay 4=1/# 4#00

1#. peratin' ?F 4= 8 / 5 11!.#5 11. 111. 10".$5 108.5! 10$.! 10$.00

1. )er(inal ?F 4 = " /10 "8

1. J ? F 4#00 11!.#5 11. 111. 10".$5 108.5! 10$.!$ #05

4c &RR 4r of the proHect can +e o+tained +y solvin' the followin' euation for r#00 / 11!.#5 3 9V&F 4r,1 / 11. 3 9V&F 4r,#

/ 111. 3 9V&F 4r, / 10".$5 3 9V&F 4r, / 108.5! 3 9V&F 4r,5

$


38/164

/10$.!$ 3 9V&F 4r,! / #05 3 9V&F 4r,$ = 0

)hrou'h a process of trial and error, we 'et r = 55.1$%. )he &RR of the proHect is 55.1$%.

#. Post-ta# Incremental Cash 'lo0s Rs1 in million!

Year 2 3 4 5 6 7 8 9

1. ?apital euip(ent 41#0#. 6evel of worin' capital #0 0 0 50 0 0 #0 4endin'

. Revenues 80 1#0 1!0 #00 1!0 1#0 80. Raw (aterial cost # ! 8 !0 8 ! #5. Varia+le (f' cost. 8 1# 1! #0 1! 1# 8!. Fi3ed operatin' X (aint. 10 10 10 10 10 10 10 cost$. Varia+le sellin' e3penses 8 1# 1! #0 1! 1# 88. &ncre(ental overheads ! 8 10 8 ! ". 6oss of contri+ution 10 10 10 10 10 10 10

10.>ad de+t loss 11. Bepreciation 0 ##.5 1!.88 1#.!! "." $.1# 5.1#. 9rofit +efore ta3 1 11.5 5.1# 5$. #.51 #!.88 !.!!1. )a3 .# .5 10.5 1$.#0 1#.$5 8.0! #.001. 9rofit after ta3 ".8 8.05 #.58 0.1 #".$! 18.8# .!!15. Jet salva'e value of capital euip(ents #51!. Recovery of worin' 1!

capital1$. &nitial invest(ent 41#018. peratin' cash flow #0.# 0.55 1.! 5#.80 ".#5 #5." 1.00

41 / 10/ 11

1". Iorin' capital #0 10 10 10 410 410 410#0. )er(inal cash flow 1

#1. Jet cash flow 410 10.#0 #0.55 1.! !#.80 ".#5 5." 55.00

41$/181"/#0

4+ J9V of the net cash flow strea( U 15% per discount rate

= 10 / 10.#0 3 9V&F415,1 / #0.55 3 9V&F 415,#/ 1.! 3 9V&F 415, / !#.80 3 9V&F 415, / ".#5 3 9V&F 415,5/ 5." 3 9V&F 415,! / 55 3 9V&F 415,$

= Rs.1.$0 (illion

8


39/164

.4a . &nitial outlay 4)i(e 0

i. ?ost of new (achine Rs. ,000,000ii. 2alva'e value of old (achine "00,000iii &ncre(ental worin' capital reuire(ent 500,000iv. )otal net invest(ent 4=i ii / iii #,!00,000

>. peratin' cash flow 4years 1 throu'h 5

Year 3 4 5 6 7

i. 9ostta3 savin's in (anufacturin' costs 55,000 55,000 55,000 55,000 55,000

ii. &ncre(ental depreciation 550,000 1#,500 0",$5 ##,01 1$,0#

iii. )a3 shield on

incre(ental dep. 1!5,000 1#,$50 "#,81 !",!0" 5#,#0$iv. peratin' cash flow 4 i / iii !#0,000 5$8,$50 5$,81 5#,!0" 50$,#0$

?. )er(inal cash flow 4year 5

i. 2alva'e value of new (achine Rs. 1,500,000ii. 2alva'e value of old (achine #00,000

iii. Recovery of incre(ental worin' capital 500,000iv. )er(inal cash flow 4 i ii / iii 1,800,000

B. Jet cash flows associated with the replace(ent proHect 4in Rs

Year 2 3 4 5 6 7

J?F 4#,!00,000 !#0000 5$8$50 5$81 5#!0" #0$#0$

4+ J9V of the replace(ent proHect= #!00000 / !#0000 3 9V&F 41,1 / 5$8$50 3 9V&F 41,# / 5$81 3 9V&F 41, / 5#!0" 3 9V&F 41, / #0$#0$ 3 9V&F 41,5

= Rs.#!$8"

"


40/164

. )a3 shield 4savin's on depreciation 4in RsDepreciation ,a# shield P+ o) ta# shield

Year charge DC! :216 # DC ; 37. p1a1

1 #5000 10000 8!"!

# 18$50 $500 5!$1

10! 5!#5 !""

105$ #1" #1#

5 $"10 1! 15$

##051

9resent value of the ta3 savin's on account of depreciation = Rs.##051

5. . &nitial outlay 4at ti(e 0i. ?ost of new (achine Rs. 00,000ii. 2alva'e value of the old (achine "0,000iii. Jet invest(ent 10,000

>. peratin' cash flow 4years 1 throu'h 5

Year 3 4 5 6 7i. Bepreciation of old (achine 18000 100 115#0 "#1! $$

ii. Bepreciationof new (achine 100000 $5000 5!#50 #188 1!1

iii. &ncre(ental

depreciation4 ii i 8#000 !0!00 $0 #"$# ##!8

iv. )a3 savin's onincre(entaldepreciation4 0.5 3 4iii #8$00 #1#10 15!5! 1150 8"

v. peratin' cash

0


41/164

flow #8$00 #1#10 15!5! 1150 8"?. )er(inal cash flow 4year 5

i. 2alva'e value of new (achine Rs. #5000ii. 2alva'e value of old (achine 10000iii. &ncre(ental salva'e value of new

(achine = )er(inal cash flow 15000

B. Jet cash flows associated with the replace(ent proposal.

Year 2 3 4 5 6 7

J?F 410000 #8$00 #1#10 15!5! 1150 #"

MINICASE

Solution:

a. ?ash flows fro( the point of all investors 4which is also called the e3plicit cost funds point of

view Rs1in million

Item 0 1 # 5

1. Fi3ed assets 415#. Jet worin'

capital 48. Revenues 0 0 0 0 0. ?osts 4other than depreciation and

interest #0 #0 #0 #0 #05. 6oss of rental 1 1 1 1 1!. Bepreciation .$50 #.81 #.10" 1.58# 1.18$$. 9rofit +efore ta3 5.#50 !.18$ !.8"1 $.18 $.81

8. )a3 1.5$5 1.85! #.0!$ #.##5 #.". 9rofit after ta3 .!$5 .1 .8# 5.1" 5.!"10. 2alva'e value of fi3ed assets 5.00011. Jet recovery of worin' capital 8.0001#. &nitial outlay 4#1. peratin' cash

1


42/164

inflow $.#5 $.1 !." !.$$5 !.!5!1. )er(inal cash flow 1.000

15. Jet cash flow 4# $.#5 $.1 !." !.$$5 1".!5!

+. ?ash flows for( the point of euity investors

Rs1in million

Item 0 1 # 5

1. uity funds 410#. Revenues 0 0 0 0 0. ?osts 4other than depreciation and

interest #0 #0 #0 #0 #0. 6oss of rental 1 1 1 1 15. Bepreciation .$5 #.81 #.10" 1.58# 1.18$

!. &nterest on worin'capital advance 0.$0 0.$0 0.$0 0.$0 0.$0

$. &nterest on ter( loans 1.#0 1.1#5 0.8#5 0.5#5 0.##58. 9rofit +efore ta3 .5 .!# 5.!! !.1" !.888". )a3 1.005 1.0" 1.!10 1.858 #.0!!10. 9rofit after ta3 #.5 .05 .$5! .5 .8##11. Jet salva'e value

of fi3ed assets 5.0001#. Jet salva'e value of current assets 10.0001. Repay(ent of ter( ter( loans #.000 #.000 #.000 #.0001. Repay(ent of +an advance 5.00015. Retire(ent of trade

creditors #.0001!. &nitial invest(ent 4101$. peratin' cash inflow !.0"5 5.8!! 5.8!5 5."1$ !.00"18. 6iuidation and retire(ent cash flows 4#.0 4#.0 4#.0 !.001". Jet cash flow 410 !.0"5 .8!! .8!5 ."1$ 1#.00"

#


43/164

Chapter $1

#IS! ANALYSIS IN CA&ITAL BUETIN

1.4a J9V of the proHect = #50 / 50 3 9V&F 41,10

= Rs.#1.1 (illion

4+ J9Vs under alternative scenarios:Rs1 in million!

Pessimistic E#pected "ptimistic

&nvest(ent 00 #50 #002ales 150 #00 #$5Varia+le costs "$.5 1#0 15

Fi3ed costs 0 #0 15Bepreciation 0 #5 #09reta3 profit $.5 5 8!)a3 U #8.5$% #.1 10 #.5$9rofit after ta3 5.! #5 !1.Jet cash flow #.! 50 81.?ost of capital 1% 1% 1#%

J9V 1$1.$ #1.1 #!0.10

ssu(ptions: 41 )he useful life is assu(ed to +e 10 years under all threescenarios. &t is also assu(ed that the salva'e value of the

invest(ent after ten years is Yero.

4# )he invest(ent is assu(ed to +e depreciated at 10% per annu(N and itis also assu(ed that this (ethod and rate of depreciation are

accepta+le to the &) 4inco(e ta3 authorities.

4 )he ta3 rate has +een calculated fro( the 'iven ta+le i.e. 10 - 5 3 100= #8.5$%.

4 &t is assu(ed that only loss on this proHect can +e offset a'ainst theta3a+le profit on other proHects of the co(panyN and thus the co(panycan clai( a ta3 shield on the loss in the sa(e year.


44/164

4c Accounting brea< e$en point under =e#pected> scenario!Fi3ed costs / depreciation = Rs. 5 (illion?ontri+ution (ar'in ratio = !0 - #00 = 0.

>rea even level of sales = 5 - 0. = Rs.150 (illion

'inancial brea< e$en point under =#pected> scenario!

i. nnual net cash flow = 0.$1 @ 0. 3 sales 5 A / #5= 0.#1 sales $.1

ii. 9V 4net cash flows = @0.#1 sales $.1 A 3 9V&F 41,10

= 1.1!#8 sales 8.$

iii. &nitial invest(ent = #00

iv. Financial +rea even levelof sales = #8.$ - 1.1!#8 = Rs.#05.1 (illion

#.

4a 2ensitivity of J9V with respect to uantity (anufactured and sold:in Rs!


&nitial invest(ent 0000 0000 00002ale revenue #000 #000 5000Varia+le costs 1!000 #8000 !000Fi3ed costs 000 000 000

Bepreciation #000 #000 #0009rofit +efore ta3 000 "000 1000)a3 1500 500 !5009rofit after ta3 1500 500 !500Jet cash flow 500 !500 8500J9V at a cost ofcapital of 10% p.aand useful life of

5 years 1!$# 5!0 ####

4+ 2ensitivity of J9V with respect to variations in unit price.


&nitial invest(ent 0000 0000 00002ale revenue #8000 #000 $0000


45/164

Varia+le costs #8000 #8000 #8000Fi3ed costs 000 000 000Bepreciation #000 #000 #000

9rofit +efore ta3 5000 "000 $000)a3 #500 500 185009rofit after ta3 #500 500 18500Jet cash flow 500 !500 #0500J9V 18"5 4 5!0 $$11

4c 2ensitivity of J9V with respect to variations in unit varia+le cost.


&nitial invest(ent 0000 0000 00002ale revenue #000 #000 #000Varia+le costs 5!000 #8000 #1000Fi3ed costs 000 000 000Bepreciation #000 #000 #0009rofit +efore ta3 11000 "000 1!000

)a3 5500 500 80009rofit after ta3 5500 500 8000Jet cash flow 500 !500 10000J9V #!8 5!0 $"08

d! Accounting brea


46/164

= 5.8

A = 3 0. / 3 0.5 / 5 3 0.#

= ."

J9V = .$ - 1.1 /5.8 - 41.1#/ ." - 41.1 10= Rs.#.00 (illion

1# = 0.1

## = 0.5!

# = 0."

1# ## #

#J9V = / / 41.1# 41.1 41.1!

= 1.00

4J9V = Rs.1.00 (illion

. 3pected J9V At

= #5,000

t=1 41.08t

= 1#,000-41.08 / 10,000 - 41.08#/ ",000 - 41.08

/ 8,000 - 41.08

#5,000

= @ 1#,000 3 ."#! / 10,000 3 .85$ / ",000 3 .$" / 8,000 3 .$5A #5,000

= $,$08

2tandard deviation of J9V

t

t=1 41.08t

= 5,000 - 41.08 / !,000 - 41.08#/ 5,000 - 41,08/ !,000 - 41.08

= 5,000 3 ."#! / !,000 3 .85$ / 5000 3 .$" / !,000 3 .$5= 18,15#

5. 3pected J9V

!


47/164

At= 10,000 T. 41

t=1 41.0!t

A1 = #,000 3 0.# / ,000 3 0.5 / ,000 3 0.= ,100

A# = ,000 3 0. / ,000 3 0. / 5,000 3 0.= ,"00

A = ,000 3 0. / 5,000 3 0.5 / !,000 3 0.#= ,"00

A = #,000 3 0.# / ,000 3 0. / ,000 3 0.= ,#00

2u+stitutin' these values in 41 we 'et

3pected J9V = J9V

= ,100 - 41.0!/ ,"00 - 1.0!# / ,"00 - 41.0! / ,#00 - 41,0!- 10,000 = Rs.,0

)he variance of J9V is 'iven +y the e3pression

#t# 4J9V = TT.. 4#

t=1 41.0!#t

1# = @4#,000 ,100#3 0.# / 4,000 ,100# 3 0.5/ 4,000 ,100#3 0.A

= "0,000

## = @4,000 ,"00#3 0. / 4,000 ,"00# 3 0./ 45,000 "00#3 0.A

= !"0,000

# = @4,000 ,"00#3 0. / 45,000 ,"00#3 0.5/ 4!,000 ,"00# 3 0.#A

= "0,000

# = @4#,000 ,#00#3 0.# / 4,000 ,#00#3 0./ 4,000 #00# 3 0.A

= 5!0,000

$


48/164

2u+stitutin' these values in 4# we 'et"0,000 - 41.0!#/ !"0,000 - 41.0!

/ "0,000 - 41.0!!/ 5!0,000 - 41.088

@ "0,000 3 0.8"0 / !"0,000 3 0.$"#/ "0,000 3 0.$05 / 5!0,000 3 0.!#$ A= 1,!$",150

J9V = 1,!$",150 = Rs.1,#"!

J9V J9V 0 J9V9ro+ 4J9V Z 0 = 9ro+. Z

J9V J9V 0 0

= 9ro+ [ Z 1#"!

= 9ro+ 4[ Z #.5

)he reuired pro+a+ility is 'iven +y the shaded area in the followin' nor(al curve.

P4[ Z #.5 = 0.5 P4#.5 Z?Z 0= 0.5 P40 Z?Z #.5= 0.5 0."0!= 0.00"

2o the pro+a+ility of J9V +ein' ne'ative is 0.00"

9ro+ 4P1 1.# 9ro+ 49V -I 1.#

9ro+ 4J9V -I 0.#9ro+. 4J9V 0.# 3 10,0009ro+ 4J9V #,000

9ro+ 4J9V #,000= 9ro+ 4? #,000 ,0 - 1,#"!9ro+ 4? 0.81

)he reuired pro+a+ility is 'iven +y the shaded area of the followin' nor(al

curve:P4? 0.81 = 0.5 /P40.81 Z?Z 0

= 0.5 /P40 Z?Z 0.81= 0.5 / 0.#"10= 0.$"10

2o the pro+a+ility ofP1 1.# as 0.$"10

8


49/164

!. Miven values of varia+les other than ,Pand +, the net present value (odel of >idhan?orporation can +e e3pressed as:

@4P + ,000 #,000A 40.5/ #,000 05

J9V / 0,000t=1 41.1t 41.15

0.5 4P + 500

5

= 0,000 t=1 41.1t

= @ 0.54P + 500A 3 9V&F 410,5 0,000= @0.54P + 500A 3 .$"1 0,000= 1.8"554P + 1,8"5.5

3hi+it 1 presents the correspondence +etween the values of e3o'enous varia+les and the two

di'it rando( nu(+er. 3hi+it # shows the results of the si(ulation.3hi+it 1

Corre2pon3en+e 4et5een 6alue2 o eo9enou2 6aria4le2 an3

t5o 3i9it ran3o nu4er2

@A*,I,Y PRICE +ARIABLE C"S,

+alue

Prob

Cumulati

$e Prob1

,0o digit

random

numbers +alue

Prob

Cumulati

$e Prob1

,0o digit

random

numbers +alue Prob

Cum

u-lati$e

Prob1

,0o digit

random

numbers

800 0.10

0.10 00 to 0" #0 0.0

0.0 00 to " 15 0.0

0.0 00 to #"

1,000

0.10

0.#0 10 to 1" 0 0.0

0.80 0 to $" #0 0.50

0.80 0 to $"

1,#0

0

0.#

0

0.0 #0 to " 0 0.1

0

0."0 80 to 8" 0 0.#

0

1.00 80 to ""

1,00

0.0

0.$0 0 to !" 50 0.10

1.00 "0 to ""

1,!00

0.#0

0."0 $0 to 8"

1,800

0.10

1.00 "0 to ""

"


50/164

3hi+it #Siulation #e2ult2

@A*,I,Y ! PRICE P! +ARIABLE C"S, +! *P+ Ru

n

Rando

m

*umb

er

Corres-

ponding

+alue

Random

*umber

Corres-

ponding

$alue

Rando

m

*umbe

r

Corres-

pondin

g $alue

1.8"55P-+!1,8"5.5

1 0 800 8 #0 1$ 15 #,1

# # 1,#00 !" 0 # 15 #,##

!1 1,00 0 #0 0 15 18,!#$

8 1,00 !0 0 8 0 58,5 # 1,#00 1" #0 11 15 #0,5#

! 1 1,#00 88 0 0 #0 1,5"$

$ ## 1,#00 $8 0 1 #0 ",150

8 ! 1,00 11 #0 5# #0 1,8"!

" 5$ 1,00 #0 #0 15 15 18,!#$

@A*,I,Y ! PRICE P! +ARIABLE C"S, +! *P+

Ru

n

Rando

m*umb

er

Corres-

ponding+alue

Random

*umber

Corres-

ponding$alue

Rando

m*umbe

r

Corres-

ponding $alue

1.8"55 P-+

1,8"5.5

10 "# 1,800 $$ 0 8 #0 #,##

11 #5 1,#00 !5 0 ! #0 ",150

1# ! 1,00 0 #0 8 0 8,"$0

1 1 1,000 51 0 $# #0 1#,"1

1 05 800 " #0 81 0 !#,##

15 0$ 800 "0 50 0 #0 1,5"$1! 1,#00 ! 0 !$ #0 ",150

1$ $" 1,!00 "1 50 "" 0 1,5!8

18 55 1,00 5 0 ! #0 5,5"

1" 5$ 1,00 1# #0 1" 15 18,!#$

#0 5 1,00 $8 0 ## 15 $,"10

#1 ! 1,#00 $" 0 "! 0 5,!#

## # 1,#00 ## #0 $5 #0 1,8"!

# " 1,00 " 50 88 0 5,5"

# #1 1,#00 8 0 5 #0 1,5"$

#5 08 .800 $0 0 #$ 15 ",150

#! 85 1,!00 ! 0 !" #0 1,5!8

#$ !1 1,00 !8 0 1! 15 $,"10

#8 #5 1,#00 81 0 " #0 1,5"$

#" 51 1,00 $! 0 8 #0 5,5"

0 # 1,#00 $ 0 ! #0 ",150

50


51/164

1 5# 1,00 !1 0 58 #0 5,5"

# $! 1,!00 18 #0 1 #0 1,8"!

1,00 0 #0 " #0 1,8"!

$0 1,!00 11 #0 5" #0 1,8"!5 !$ 1,00 5 #0 #! 15 18,!#$

! #! 1,#00 ! 0 ## 15 #,##

@A*,I,Y ! PRICE P! +ARIABLE C"S, +! *P+

Ru

n

Random

*umber

Corre

s-pondi

ng

+alue

Random

*umber

Corres-

ponding$alue

Rando

m*umbe

r

Corres-

ponding $alue

1.8"55 P-+

1,8"5.5

$ 8" 1,!00 8! 0 5" #0 #8,$!1

8 " 1,800 00 #0 #5 15 1,8!

" 0" .800 15 #0 #" 15 #,1

0 1,00 8 0 #1 15 ,$

1 "8 1,800 # #0 $" #0 1,8"!# 10 1,000 5 0 $$ #0 1#,"1

8 1,#00 0 1 #0 ",150

8 1,!00 0 #0 10 15 1!,$#

5 5 1,00 $1 0 5# #0 5,5"

! 1! 1,000 $0 0 1" 15 ,!

$ #0 1,#00 !5 0 8$ 0 5,!#

8 !1 1,00 !1 0 $0 #0 5,5"

" 8# 1,!00 8 0 "$ 0 !#,##

50 "0 1,800 50 0 #0 #,##

3pected J9V = J9V50

= 1- 50 J9Vii=1

= 1-50 4$,#0,"!1= 1,1"

50

Variance of J9V = 1-50 (J9Vi J9V#

i=1

= 1-50 @#$,$.0$ 3 10!A= 5".81 3 10!

51


52/164

2tandard deviation of J9V = 5".81 3 10!

= #,1

$. )o carry out a sensitivity analysis, we have to define the ran'e and the (ost liely values ofthe varia+les in the J9V ;odel. )hese values are defined +elow

+ariable Range &ost li


53/164

800 1,000 1,#00 1,00 1,!00 1,800*P+ 1!,$# 1#,"1 ",150 5,5" 1,5!8 #,##

Sensiti$ity analysis 0ith re)erence to P

)he relationship +etweenPand*P+, 'iven the (ost liely values of other varia+les is defined asfollows:

5 @1,00 4P#0 ,000 #,000A 3 0.5 / #,000 0

*P+ = / 0,0

t:1 41.1t 41.15

5 $00P 1,500

= 0,000 t=1 41.1t

)he net present values for various values ofPare 'iven +elow :

P4Rs #0 0 0 50*P+4Rs 1,8"! 5,5" #1,1$" $,$1!

8. *P+ 5 0 5 10 15 #04Rs.in lahsPI 0." 1.00 1.10 1.#0 1.0 1.0

9ro+. 0.0# 0.0 0.10 0.0 0.0 0.15

!

3pectedPI=PI = 4PI/P/ /=1= 1.#

!

2tandard deviation ofP1= 4PI/ PI#P/

/=1= .0115!= .10$5

)he standard deviation ofP1is .10$5 for the 'iven invest(ent with an e3pected PIof 1.#.)he (a3i(u( standard deviation ofPIaccepta+le to the co(pany for an invest(ent with ane3pectedPIof 1.#5 is 0.0.

5


54/164

2ince the ris associated with the invest(ent is (uch less than the (a3i(u( ris accepta+leto the co(pany for the 'iven level of e3pectedPI, the co(pany (ust should accept theinvest(ent.

". )he J9Vs of the two proHects calculated at their ris adHusted discount rates are as follows: ! ,000

9roHectA: J9V = 10,000 = Rs.#,t=1 41.1#t

5 11,000

9roHectB: J9V = 0,000 = Rs.$,$!

t=1 41.1t

PI andIRRfor the two proHects are as follows:

Pro/ect A B

PI 1.# 1.#!IRR #0% #.%

Bis superior toAin ter(s of*P+,PI, andIRR. *ence the co(pany (ust chooseB.

10. )he certainty euivalent coefficients for the five years are as follows

Year Certainty eui$alent coe))icient

t= 1 0.0! t

1 1= 0."# # = 0.88 = 0.8#4 = 0.$!5 5 = 0.$0

)he present value of the proHect calculated at the risfree rate of return is :5 41 0.0! t At t=1 41.08t

$,000 3 0." 8,000 3 0.88 ",000 3 0.8# 10,000 3 0.$! 8,000 3 0.$0 / / / /

41.08 41.08# 41.08 41.08 41.085

5


55/164

!,580 $,00 $,80 $,!00 5,!00 / / / /

41.08 41.08# 41.08 41.08 41.085

= #$,8!

Jet present value of the 9roHect = 4#$,8! 0,000= Rs. #,!1

MINICASE

Solution:

1. )he e3pected J9V of the tur+oprop aircraft

0.!5 45500 / 0.5 4500J9V = 11000 /

41.1#

0.!5 @0.8 41$500 / 0.# 4000A / 0.5 @0. 41$500 / 0.! 4000A/41.1##

= #!"

#. &f 2outhern irways +uys the piston en'ine aircraft and the de(and in year 1 turns out to +e

hi'h, a further decision has to +e (ade with respect to capacity e3pansion. )o evaluate thepiston en'ine aircraft, proceed as follows:

First, calculate the J9V of the two options viY., e3pandE and do not e3pandE at decisionpoint B#:

0.8 415000 / 0.# 41!003pand : J9V = 00 /

1.1#

= !!00

0.8 4!500 / 0.# 4#00Bo not e3pand : J9V =

1.1#= 50$1

55


56/164

2econd, truncate the do not e3pandE option as it is inferior to the e3pandE option. )his(eans that the J9V at decision point B#will +e !!00

)hird, calculate the J9V of the piston en'ine aircraft option.

0.!5 4#500/!!00 / 0.5 4800J9V = 5500 /

1.1#

0.5 @0.# 4!500 / 0.8 4#00A /

41.1##

= 5500 / 551 / 8"8 = "#"

. )he value of the option to e#pandin the case of piston en'ine aircraft

&f 2outhern irways does not have the option of e3pandin' capacity at the end of year 1, theJ9V of the piston en'ine aircraft would +e:

0.!5 4#500 / 0.5 4800J9V = 5500 /

1.1#

0.!5 @0.8 4!500 / 0.# 4#00A / 0.5 @0.# 4!500 / 0.8 4#00A

/ 41.1##

= 5500 / 1$01 / 8# =

)hus the option to e#pandhas a value of "#" = 88!

. Value of the option to abandonif the tur+oprop aircraft can +e sold for 8000 at the end of year1

&f the de(and in year 1 turns out to +e low, the payoffs for the continuationE anda+andon(entE options as of year 1 are as follows.

0. 41$500 / 0.! 4000?ontinuation: = $85$

1.1#

5!


57/164

+andon(ent : 8000

)hus it (aes sense to sell off the aircraft after year 1, if the de(and in year 1 turns out to +e

low.

)he J9V of the tur+oprop aircraft with a+andon(ent possi+ility is

0.!5 @5500 /\0.8 41$500 / 0.# 4000]- 41.1#A / 0.5 4500 /8000J9V = 11,000 /

41.1#

1#08 / #"$5 = 11,000 / = #1

1.1#

2ince the tur+oprop aircraft without the a+andon(ent option has a value of #!", thevalue of the a+andon(ent option is : #1 #!" =

5. )he value of the option to abandonif the piston en'ine aircraft can +e sold for 00 at the

end of year 1:

&f the de(and in year 1 turns out to +e low, the payoffs for the continuationE anda+andon(entE options as of year 1 are as follows:

0.# 4!500 / 0.8 4#00?ontinuation : = #8$5

1.1#

+andon(ent : 00

)hus, it (aes sense to sell off the aircraft after year 1, if the de(and in year 1 turns out to+e low.

)he J9V of the piston en'ine aircraft with a+andon(ent possi+ility is:

0.!5 @#500 / !!00A / 0.5 @800 / 00AJ9V = 5500 /

1.1#

5"15 / 18#0 = 5500 / = 10!

1.1#

For the piston en'ine aircraft the possi+ility of a+andon(ent increases the J9V

5$


58/164

fro( "#" to 10!. *ence the value of the a+andon(ent option is $$.

58


59/164

Chapter $;

T'E COST OF CA&ITAL

14a Befine rDas the preta3 cost of de+t. 7sin' the appro3i(ate yield for(ula, rD can +ecalculated as follows:

1 / 4100 108-10rD = 3 100 = 1#.!0%

0. 3 100 / 0.!3108

4+ fter ta3 cost = 1#.!0 3 41 0.5 = 8.1"%

#. Befine rpas the cost of preference capital. 7sin' the appro3i(ate yield for(ularp can +ecalculated as follows:

" / 4100 "#-!rp =

0. 3100 / 0.!3"#

= 0.1085 4or 10.85%

. I?? = 0. 3 1% 3 41 0.5/ 0.! 3 18%

= 1.18%

. ?ost of euity = 10% / 1.# 3 $% = 18.%4usin' 2;6 euation

9reta3 cost of de+t = 1%

fterta3 cost of de+t = 1% 3 41 0.5 = ".1%

Be+t euity ratio = # :

I?? = #-5 3 ".1% / -5 3 18.%

= 1.!8%

5. Miven0.5 3 1% 3 41 0.5 / 0.5 3 rE= 1#%

where rEis the cost of euity capital.

)herefore rE 1."%

5"


60/164

7sin' the 2;6 euation we 'et

11% / 8% 3 = 1."%

where O denotes the +eta of YeeYEs euity.

2olvin' this euation we 'et O = 0.8$5.

!4a )he cost of de+t of 1#% represents the historical interest rate at the ti(e the de+t wasori'inally issued. >ut we need to calculate the (ar'inal cost of de+t 4cost of raisin' new

de+tN and for this purpose we need to calculate the yield to (aturity of the de+t as on the+alance sheet date. )he yield to (aturity will not +e eual to1#% unless the +oo value ofde+t is eual to the (aret value of de+t on the +alance sheet date.

4+ )he cost of euity has +een taen asD1-P04 = !-100 whereas the cost of euity is 4D1-P0/gwhere grepresents the e3pected constant 'rowth rate in dividend per share.

$. )he +oo value and (aret values of the different sources of finance are

provided in the followin' ta+le. )he +oo value wei'hts and the (aret valuewei'hts are provided within parenthesis in the ta+le.Rs1 in million!

Source Boo< $alue &ar


61/164

acceptin' or reHectin' the proHects would +e to co(pare the e3pected rate of return and thereuired rate of return for each proHect. >ased on this co(parison, we find that all the fourproHects need to +e reHected.

".4a Miven

rD3 41 0. 3 -" / #0% 3 5-" = 15%rD = 1#.5%,where rD represents the preta3 cost of de+t.

4+ Miven1% 3 41 0. 3 -" / rE 3 5-" = 15%rE = 1".$#%, where rErepresents the cost of euity.

10. ?ost of euity = D1-P0/g = .00 - 0.00 / 0.05 = 15%

4a )he first chun of financin' will co(prise of Rs.5 (illion of retained earnin's costin' 15percent and Rs.#5 (illion of de+t costin' 1 41. = ".8 per cent)he second chun of financin' will co(prise of Rs.5 (illion of additional euity costin'

15 per cent and Rs.#.5 (illion of de+t costin' 15 41. = 10.5 per cent

4+ )he (ar'inal cost of capital in the first chun will +e :5-$.5 3 15% / #.5-$.5 3 ".8% = 1.#$%)he (ar'inal cost of capital in the second chun will +e:

5-$.5 3 15% / #.5-$.5 3 10.5% = 1.50%

Jote : Ie have assu(ed that4i )he net realisation per share will +e Rs.#5, after floatation costs, and4ii )he planned invest(ent of Rs.15 (illion is inclusive of floatation costs

11. )he cost of euity and retained earnin'srE = D1-P/g

= 1.50 - #0.00 / 0.0$ = 1.5%)he cost of preference capital, usin' the appro3i(ate for(ula, is :

11 / 4100$5-10rE = = 15."%

0.! 3 $5 / 0. 3 100

!1


62/164

)he preta3 cost of de+entures, usin' the appro3i(ate for(ula, is :

1.5 / 410080-!

rD = = 1".1%0.!380 / 0.3100

)he postta3 cost of de+entures is1".1 41ta3 rate = 1".1 41 0.5

= ".!%

)he postta3 cost of ter( loans is

1# 41ta3 rate = 1# 41 0.5 = !.0%

)he avera'e cost of capital usin' +oo value proportions is calculated +elow :

Source o) capital Component Boo< $alue Boo< $alue Product o)

Cost Rs1 in million proportion 41 X 4 41 4# 4

uity capital 1.5% 100 0.#8 .0!9reference capital 15."% 10 0.0 0.8Retained earnin's 1.5% 1#0 0. .$"Be+entures ".!% 50 0.1 1.)er( loans !.0% 80 0.## 1.#

!0 vera'e cost11.""% capital

)he avera'e cost of capital usin' (aret value proportions is calculated +elow :

Source o) capital Component &ar


63/164

4a I?? = 1- 3 1% 3 41 0./ #- 3 #0%

= 1!.$%

4+ Iei'hted avera'e floatation cost= 1- 3 % / #- 3 1#%= "%

4c J9V of the proposal after tain' into account the floatation costs= 10 3 9V&F 41!.$, 8 500 - 41 0.0"

= Rs.8.51 (illion

MINICASE

Solution:

a. ll sources other than noninterest +earin' lia+ilities

+. 9reta3 cost of de+t X postta3 cost of de+t

10 / 4100 11# - 8 8.5rd= = = $."

0.! 3 11# / 0. 3 100 10$.#

rd 41 0. = 5.55

c. 9ostta3 cost of preference" / 4100 10! - 5 $.8

= = $.5%0.! 3 10! / 0. 3 100 10.!

d. ?ost of euity usin' the BB;

#.80 41.10 / 0.10 = 0.85 / 0.10

80= 0.185 = 1.85%

e. ?ost of euity usin' the ?9;

$ / 1.14$ = 1.$0%

f. I??0.50 3 1.$0 / 0.10 3 $.5 / 0.0 3 5.55

!


64/164

= $.5 / 0.$5 / #.##= 10.#%

'. ?ost of capital for the new +usiness

0.5 @$ / 1.5 4$A / 0.5 @ 11 41 0.A8.$5 / .85= 1#.!0%

!


65/164

Chapter $

2ince 4> Z 4, the less costly overhaul is preferred alternative.

!5


66/164

.4a >ase case J9V

= 1#,000,000 / ,000,000 3 9V&F 4#0,!= 1#,000,000 / ""$,8000= 4 Rs.#,0##,000

4+ &ssue costs = !,000,000 - 0.88 !,000,000

= Rs.818 18#

dHusted J9V after adHustin' for issue costs

= #,0##,000 818,18#= Rs.#,80,18#

4c )he present value of interest ta3 shield is calculated +elow :

Year Debt outstanding at Interest ,a# shield Present $alue o) the beginning ta# shield

1 !,000,000 1,080,000 #,000 #$,5"0 # !,000,000 1,080,000 #,000 ##,!"$ 5,#50,000 "5,000 #8,000 1$#,58 ,500,000 810,000 #,000 1#5," 5 ,$50,000 !$5,000 #0#,000 88,51 ! ,000,000 50,000 1!#,000 !0,005 $ #,##5,000 00,500 1#0,000 $,$15 8 1,500,000 #$0,000 81,000 #1,5! " $50,000 15,000 0,500 ",1

9resent value of ta3 shield = Rs.1,0##,0$!

5.4a >ase case >9V

= 8,000,000 / #,000,000 3 9V&F 418,!= Rs.1,00,000

4+ dHusted J9V after adHust(ent for issue cost of e3ternal euity

= >ase case J9V &ssue cost= 1,00,000 @ ,000,000 - 0." ,000,000A= Rs.1,$,

!!


67/164

4c )he present value of interest ta3 shield is calculated +elow :

Year Debt outstanding at Interest ,a# shield Present $alue o)

the beginning ta# shield 1 5,000,000 $50,000 00,000 #!0,880 # 5,000,000 $50,000 00,000 ##!,80 ,000,000 !00,000 #0,000 15$,800 ,000,000 50,000 180,000 10#,"# 5 #,000,000 00,000 1#0,000 5",!! ! 1,000,000 150,000 !0,000 #5,"8

9resent value of ta3 shield = Rs.8,0!

!$


68/164

Chapter $8

#AISIN LON TE#M FINANCE

1 @nder0riting Shares E#cess% Credit *et commitment procured short)all short)all

A $0,000 50,000 4#0,000 "1" 415081

B 50,000 0,000 4#0,000 51 41!8!

C 0,000 0,000 410,000 #811 4$18"

D #5,000 1#,000 41,000 1$5$ 411#

E 15,000 #8,000 1,000

#.@nder0riting Shares E#cess% Credit *et

commitment procured Short)all short)all

A 50,000 #0,000 40,000 1#8! 415$1

B #0,000 10,000 410,000 5$1 4#8!

C 0,000 50,000 #0,000

. Po= Rs.##0 S= Rs.150 * = a. )he theoretical value per share of the cu(ri'hts stoc would si(ply +e

Rs.##0

+. )he theoretical value per share of the e3ri'hts stoc is :

!8


69/164

*PoS 3 ##0 /150 = = Rs.#0!

*/1 /1

c. )he theoretical value of each ri'ht is :Po S ##0 150

= = Rs.1*/1 /1

)he theoretical value of ri'hts which are reuired to +uy 1 share is Rs.131=Rs.5!.

. Po= Rs.180 *= 5a. )he theoretical value of a ri'ht if the su+scription price is Rs.150

Po S 180 150 = = Rs.5

*3 5/1

+. )he e3ri'hts value per share if the su+scription price is Rs.1!0*Po S 5 3 180 / 1!0 = = Rs.1$!.$

*/1 5/1

c. )he theoretical value per share, e3ri'hts, if the su+scription price isRs.180G 100G

5 3 180 / 180 = Rs.180

5/1

5 3 180 / 100 = Rs.1!!.$

5/1

!"


70/164

Chapter $"

CA&ITAL ST#UCTU#E AN FI#M VALUE

1. Jet operatin' inco(e "! : Rs.0 (illion&nterest on de+t 4I! : Rs.10 (illion

uity earnin's 4P! : Rs.#0 (illion?ost of euity 4rE! : 15%

?ost of de+t 4rD : 10%;aret value of euity 4E : Rs.#0 (illion-0.15 =Rs.1 (illion;aret value of de+t 4D! : Rs.10 (illion-0.10 =Rs.100 (illion;aret value of the fir( + : Rs.# (illion

#. Bo# Co#;aret value of euity #,000,000-0.15 #,000,000-0.15

= Rs.1. (illion = Rs.1. (illion;aret value of de+t 0 1,000,000-0.10

=Rs.10 (illion;aret value of the fir( Rs.1.(illion =#. (illion

4a vera'e cost of capital for >o3 ?orporation1.. 0

3 15% / 3 10% = 15%1. 1.

vera'e cost of capital for ?o3 ?orporation 1. 10.00

3 15% / 3 10% = 1#.8!%#. #.

4+ &f >o3 ?orporation e(ploys Rs.0 (illion of de+t to finance a proHect that yieldsRs. (illion net operatin' inco(e, its financials will +e as follows.

Jet operatin' inco(e Rs.!,000,000&nterest on de+t Rs.,000,000uity earnin's Rs.,000,000?ost of euity 15%

$0


71/164

?ost of de+t 10%;aret value of euity Rs.#0 (illion;aret value of de+t Rs.0 (illion

;aret value of the fir( Rs.50 (illion

vera'e cost of capital #0 0

15% 3 / 10% = 1#%50 50

4c &f ?o3 ?orporation sells Rs.10 (illion of additional euity to retireRs.10 (illion of de+t , it will +eco(e an alleuity co(pany. 2o its avera'e cost of capital will si(ply +e eual to its cost of euity, which is 15%.

. rE = rA / 4rA-rD!D%E #0 = 1# / 41#8D%E 2o D%E = #

. E D E DrE rD rA = rE/ rD

DE DE 4% 4% D/E D/E

1.00 0.00 11.0 !.0 11.00 0."0 0.10 11.0 !.5 10.55 0.80 0.#0 11.5 $.0 10.!0 0.$0 0.0 1#.5 $.5 11.00 0.!0 0.0 1.0 8.5 11.#0 0.50 0.50 1.0 ".5 11.$5

0.0 0.!0 15.0 11.0 1#.!0 0.0 0.$0 1!.0 1#.0 1.#0 0.#0 0.80 18.0 1.0 1.00 0.10 0."0 #0.0 1.0 1.#0

)he opti(al de+t ratio is 0.10 as it (ini(ises the wei'hted avera'e

cost of capital.

5. 4a &f you own Rs.10,000 worth of >harat ?o(pany, the levered co(pany which is valued (ore, you would sell shares of >harat ?o(pany, resort to personal levera'e, and +uy the shares of ?harat ?o(pany.

4+ )he ar+itra'e will cease when ?harat ?o(pany and >harat ?o(panyare valued alie

$1


72/164

!. )he value of shwini 6i(ited accordin' to ;odi'liani and ;iller hypothesis is

3pected operatin' inco(e 15

= = Rs.1#5 (illion Biscount rate applica+le to the 0.1# ris class to which swini +elon's$. )he avera'e cost of capital4without considerin' a'ency and +anruptcy cost at various levera'e ratios is 'iven +elow.

D E E DrD rE rA = rE / rD

D/E D/E % % D/E D/E .!

0 1.00 .0 1#.0 1#.00.10 0."0 .0 1#.0 11.#

0.#0 0.80 .0 1#.5 10.8 0.0 0.$0 .0 1.5 10.! 0.0 0.!0 .0 1.5 ".8!

0.50 0.50 .0 1.0 ".0 0.!0 0.0 .0 1.5 8.!8 0.$0 0.0 .0 15.0 8.1 0.80 0.#0 .0 15.5 $."0 0."0 0.10 .0 1!.0 7>7. Optial

+. )he avera'e cost of capital considerin' a'ency and +anruptcy costs is'iven +elow.

D E E DrD rE rA = rE / rD

D/E D/E % % D/E D/E .!

0 1.00 .0 1#.0 1#.00.10 0."0 .0 1#.0 11.#

0.#0 0.80 .0 1.0 11.#

0.0 0.$0 .# 1.0 11.0! 0.0 0.!0 . 15.0 10.$! 0.50 0.50 .! 1!.0 10.0 0.!0 0.0 .8 1$.0 ".!8 0.$0 0.0 5.# 18.0 ".0 0.80 0.#0 !.0 1".0 8.!0 0."0 0.10 !.8 #0.0 8>$. Optial8. )he ta3 advanta'e of one rupee of de+t is :

$#


73/164

141tc 41tpe 410.55 410.05 = 1

41tpd 410.#5

= 0. rupee

Chapter .%

CA&ITAL ST#UCTU#E ECISION

1.4a ?urrently Jo. of shares = 1,500,000

EBI, = Rs $.# (illion &nterest = 0 9reference dividend = Rs.1# 3 50,000 = Rs.0.! (illion EPS = Rs.#

EBI, &nterest 41-t! 9reference dividend EPS : Jo. of shares

4$,#00,000 0 41t! !00,000Rs.# =

1,500,000

*ence t = 0.5 or 50 per cent

)heEPSunder the two financin' plans is :

Finan+in9 &lan A: &ssue of 1,000,000 shares

4EBI, 0 4 1 0.5 !00,000 EPSA = #,500,000

Finan+in9 &lan B: &ssue of Rs.10 (illion de+entures carryin' 15 per centinterest

4EBI, 1,500,000 410.5 !00,000 EPSB =

1,500,000

)heEPS EBI,indifference point can +e o+tained +y euatin'EPSA andEPSB

4EBI, 0 41 0.5 !00,000 4EBI, 1,500,000 41 0.5 !00,000

$


74/164

= #,500,000 1,500,000

2olvin' the a+ove we 'etEBI,= Rs.,"50,000 and at thatEBI, EPSis Rs.0.$5 under +oth the plans

4+ s lon' asEBI,is less than Rs.,"50,000 euity financin' (a3i(i3esEPS1IhenEBI, e3ceeds Rs.,"50,000 de+t financin' (a3i(isesEPS.

#.4a EPS EBI,euation for alternativeA

EBI,4 1 0.5EPSA =#,000,000

4+ EPS EBI, euation for alternativeB EBI,4 1 0.5 0,000

EPSB = 1,!00,000

4c EPS EBI,euation for alternative C 4>&) 1,#00,000 41 0.5EPSC =

1,#00,000

4d )he three alternative plans of financin' raned in ter(s ofEPSover varyin'6evels ofEBI, are 'iven the followin' ta+le

Ran


75/164

1,800,000 4>&) 1,500,000 41 0.!

EPSB =

1,000,000

uatin'EPSA andEPSB, we 'et

4EBI, 0 41 0.! 4EBI, 1,500,000 41 0.! = 1,800,000 1,000,000

2olvin' this we 'etEBI,= ,$5,000 or .$5 (illion

)hus the de+t alternative is +etter than the euity alternative whenEBI, .$5 (illion

EBI, EBI, .$5 $.000 9ro+4EBI,,$5,000 = 9ro+

EBI, .000

= 9ro+ @ 1.#1A = 0.88!"

. R"E : F R"I R"I r ! D%E G41 t15 = @ 1 / 4 1 8 D-EA 4 1 0.5

D-E = #.!$

5. R"E= @1# / 41# " 0.! A 41 0.! = 5.5# per cent

!. 18 = F R"I R"I 8 0.$ A 4 1 0.5 R"I = #.$ per cent >&)$. a. &nterest covera'e ratio =

&nterest on de+t

150 =

0 = .$5 EBI, / Bepreciation +. ?ash flow covera'e ratio =

6oan repay(ent instal(ent

$5


76/164

&nt.on de+t / 41 )a3 rate

= 150 / 0

0 / 50

= #8. )he de+t service covera'e ratio for 9ioneer uto(o+iles 6i(ited is 'iven +y : 5

(PA, i Depi Inti i=1

DSCR = 5 (Inti LRIi!

i=1

= 1.00 / ".1 /"5.80

"5.80 / $#.00

= #$$." 1!$.80

= 1.!!

". 4a &f the entire outlay of Rs. 00 (illion is raised +y way of de+t carryin' 15 per centinterest, the interest +urden will +e Rs. 5 (illion.

?onsiderin' the interest +urden the net cash flows of the fir( durin'a recessionary year will have an e3pected value of Rs. 5 (illion 4Rs.80 (illion Rs. 5

(illion and a standard deviation of Rs. 0 (illion . 2ince the net cash flow 4( is distri+uted nor(ally( 5

0 has a standard nor(al deviation ?ash flow inadeuacy (eans that(is less than 0. 0.5

9ro+4(Z0 = 9ro+ 4Z = 9ro+ 4Z 0.8$5 0

= 0.1"0"

4+ 2ince = Rs.80 (illion, = Rs.0 (illion , and the?value correspondin' to the ristolerance li(it of 5 per cent is 1.!5, the cash availa+le fro( the operations to service thede+t is eual to(which is defined as :

( 80

$!


77/164

= 1.!5 0 ( = Rs.1.# (illion

Miven 15 per cent interest rate, the de+t than +e serviced is 1.#

= Rs. ".!$ (illion 0.15

Chapter .$

IVIEN &OLICY AN FI#M VALUE

1. Payout ratio Price per share

40.5/40.5 0.150.5

0.1# = Rs. #8.1

0.1#

40.$ 5/40.#5 0.15 0.1#

0.$5 = Rs. #!.5! 0.1#

41.00 1.00 = Rs. #5.00 0.1#

#. Payout ratio Price per share

840.#50.#5 = undefined

0.1# 0.1!40.$5 840.50

0.50 = Rs.100

0.1# 0.1!40.50 841.00

1.0 =Rs.!!.$ 0.1# 0.1! 40

$$


78/164

.

9 W

Je3t yearEs price 80 $

Bividend 0 ! ?urrent price 9 W

?apital appreciation 4809 4$W

9ostta3 capital appreciation 0."4809 0." 4$W

9ostta3 dividend inco(e 0 0.8 3 !

)otal return 0." 48099

= 1%

0." 4$W / .8W

=1%

?urrent price 4o+tained +y solvin'the precedin' euation

9 = Rs.!".# W = Rs.!8.!5

$8


79/164

Chapter ..

IVIEN ECISION

1. a. 7nder a pure residual dividend policy, the dividend per share over the yearperiod will +e as follows:

&S Un3er &ure #e2i3ual i6i3en3 &oli+?

in Rs1!

Year 3 4 5 6

arnin's 10,000 1#,000 ",000 15,000?apital e3penditure 8,000 $,000 10,000 8,000uity invest(ent ,000 ,500 5,000 ,0009ure residualdividends !,000 8,500 ,000 11,000Bividends per share 1.#0 1.$0 0.80 #.#0

+. )he e3ternal financin' reuired over the year period 4under the assu(ption that theco(pany plans to raise dividends +y 10 percents every two years is 'iven +elow :

#e@uire3 Le6el o Eternal Finan+in9

in Rs1!

Year 3 4 5 6

. Jet inco(e 10,000 1#,000 ",000 15,000

> . )ar'etedDPS 1.00 1.10 1.10 1.#1

? . )otal dividends 5,000 5,500 5,500 !,050

B . Retained earnin's4A-C 5,000 !,500 ,500 8,"50

. ?apital e3penditure 8,000 $,000 10,000 8,000

$"


80/164

F . 3ternal financin'reuire(ent ,000 500 !,500 Jil

4E-DifE H Dor 0 otherwise

c. Miven that the co(pany follows a constant !0 per cent payout ratio, the dividend per shareand e3ternal financin' reuire(ent over the year period are 'iven +elow

i6i3en3 &er Share an3 Eternal Finan+in9 #e@uireent

in Rs1!

Year 3 4 5 6

. Jet inco(e 10,000 1#,000 ",000 15,00

>. Bividends !,000 $,#00 5,00 ",000

?. Retained earnin's ,000 ,800 ,!00 !,000

B. ?apital e3penditure 8,000 $,000 10,000 8,000

. 3ternal financin'4D-CifDHC, or 0 ,000 #,#00 !,00 #,000otherwise

F. Bividends per share 1.#0 1. 1.08 1.80

#. Miven the constraints i(posed +y the (ana'e(ent, the dividend per share has to+e +etween Rs.1.00 4the dividend for the previous year and Rs.1.!0 480 percent of earnin's per share

2ince share holders have a preference for dividend, the dividend should +e raised over the previous dividend of Rs.1.00 . *owever, the fir( has su+stantial

invest(ent reuire(ents and it would +e reluctant to issue additional euity+ecause of hi'h issue costs 4 in the for( of underpricin' and floatation costs

?onsiderin' the conflictin' reuire(ents, it see(s to (ae sense to payRs.1.#0 per share +y way of dividend. 9ut differently the pay out ratio (ay +eset at !0 per cent.

. ccordin' to the 6intner (odelDt = cr EPSt / 43cDt1

EPSt :.00, c= 0.$, r=0.! and Dt-3

80


81/164

*ence Dt = 0.$ 3 0.! 3 .00 / 410.$1.#0

= Rs.1.!#

. )he +onus ratio 4b (ust satisfy the followin' constraints :4R-Sb!216S41/b 410. 9>) ^0.1 S41/b 4#

R= Rs.100 (illion, S= Rs.!0 (illion, 9>) = Rs.!0 (illion*ence the constraints are

4100!0 b ^ 0. 3 !0 41/b 41a 0. 3 !0^0.1 3 !0 41/b 4#a

)hese si(plify to

b $!-8

b #

)he condition b^ $!-8 is (ore restructive than b #2o the (a3i(u( +onus ratio is $!-8 or 1"-#1

81


82/164

Chapter .1

e4t Anal?2i2 an3 Mana9eent

1. 4i &nitial utlay4a ?ost of callin' the old +onds

Face value of the old +onds #50,000,000 ?all pre(iu( 15,000,000 #!5,000,000

4+ Jet proceeds of the new +ondsMross proceeds #50,000,000&ssue costs 10,000,000

#0,000,0004c )a3 savin's on ta3deducti+le e3penses

)a3 rate@?all pre(iu(/7na(ortised issue cost on the old +ondsA ",#00,000 0. @ 15,000,000 / 8,000,000A&nitial outlay i4a i4+ i4c 15,800,000

4ii nnual Jet ?ash 2avin's4a nnual net cash outflow on old +onds

&nterest e3pense #,500,000

- )a3 savin's on interest e3pense and a(ortisation of issue e3penses 1$,00,0000. @#,500,000 / 8,000,000-10A

#5,100,000

4+ nnual net cash outflow on new +onds&nterest e3pense $,500,000

- )a3 savin's on interest e3pense and a(ortisation of issue cost 15,500,000

0. @ $,500,000 10,000,000-8A ##,000,000

nnual net cash savin's : ii4a ii4+ ,100,000

8#

4iii 9 t V l f th l ? h 2 i


83/164

4iii 9resent Value of the nnual ?ash 2avin's9resent value of an 8year annuity of ,100,000 at adiscount rate of " per cent which is the post ta3 cost

of new +onds ,100,000 3 5.55 1$,158,500

4iv Jet 9resent Value of Refundin' the >onds4a 9resent value of annual cash savin's 1$,158,5004+ Jet initial outlay 15,800,0004c Jet present value of refundin' the +onds :

iv4a iv4+. 1,58,500#. 4i &nitial utlay

4a ?ost of callin' the old +onds Face value of the old +onds 1#0,000,000 ?all pre(iu( ,800,000

1#,800,0004+ Jet proceeds of the new issue

Mross proceeds 1#0,000,000&ssue costs #,00,000

11$,!00,000 4c )a3 savin's on ta3deducti+le e3penses ,1#0,000

)a3 rate@?all pre(iu(/7na(ortised issue costs onthe old +ond issueA 0. @ ,800,000 / ,000,000A

&nitial outlay i4a i4+ i4c ,080,000

4ii nnual Jet ?ash 2avin's

4a nnual net cash out flow on old +onds&nterest e3pense 1",#00,000

- )a3 savin's on interest e3pense and a(ortisation of issue costs $,"#0,000 0.@1",#00,000 / ,000,000-5A

11,#80,000

4+ nnual net cash outflow on new +onds

&nterest e3pense 18,000,000- )a3 savin's on interest e3pense and a(ortistion of issue costs $,"#,000

0.@18,000,000 / #,00,000-5A 10,!08,000

nnual net cash savin's : ii4a ii4+ !$#,0004iii 9resent Value of the nnual Jet ?ash 2avin's

8

9 t l f 5 it f !$# 000 t


84/164

9resent value of a 5 year annuity of !$#,000 at as discount rate of " per cent, which is the postta3 #,!1,080 cost of

new +onds

4iv Jet 9resent Value of Refundin' the >onds 4a 9resent value of annual net cash savin's #,!1,080

4+ &nitial outlay ,080,000 4c Jet present value of refundin' the +onds : 1,!!,000

iv4a iv4+

. Kield to (aturity of +ondP

8 1!0 1000 "18.50 = / t=1 41/r!t 41/r8

ror yield to (aturity is 18 percent

Kield to (aturity of +ond 5 1#0 1000

$!1 = / t=1 41/r!t 41/r5

ror yield to (aturity is #0 per cent

uration o 4on3Pi2 +al+ulate3 4elo5

Year Cash )lo0 Present +alue Proportion o) Proportion o) bond>s

at 3J. bond>s $alue +alue # ,ime

1 1!0 15.5 0.18 0.18 # 1!0 11." 0.1#5 0.#50 1!0 "$. 0.10! 0.18 1!0 8#.! 0.0"0 0.!0 5 1!0 !"." 0.0$! 0.80 ! 1!0 5".# 0.0! 0.8 $ 1!0 50.# 0.055 0.85 8 1!0 08.! 0.! #.!88

."1

uration o 4on3 Q i2 +al+ulate3 4elo5

Year Cash )lo0 Present +alue Proportion o) Proportion o) bond>s at 42. bond>s $alue +alue # ,ime

8


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1 1#0 100.0 0.11 0.11 # 1#0 8.# 0.10" 0.#18

1#0 !".5 0.0"1 0.#$ 1#0 5$.8 0.0$! 0.0 5 11#0 50.# 0.5"# #."!0

.88!

+olatility o) bond P +olatility o) bond ."1 .88!= .1! = .#

1.18 1.#0

. )he Y,& for +onds of various (aturities is

;aturity Y,&.!

1 1#.!

# 1.10

1.#1

1.8

5 1.$#

Mraphin' these Y,&s a'ainst the (aturities will 'ive the yield curve

)he one year treasury +ill rate , r1, is

1,00,000 1 = 1#.! %

8",000

)o 'et the forward rate for year #, r#, the followin' euation (ay +e set up :

1#500 11#500 ""000 = /

41.1#! 41.1#!41/r#

85

2olvin' this for r# we 'et r# = 1 "%


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2olvin' this for r#we 'et r# = 1."%

)o 'et the forward rate for year , r, the followin' euation (ay +e set up :

1,000 1,000 11,000 "",500 = / /

41.1#! 41.1#!41.1" 41.1#!41.1"41/r

2olvin' this for rwe 'et r = 1."%

)o 'et the forward rate for year , r , the followin' euation (ay +e set up :

1,500 1,500 1,500100,050 = / /

41.1#! 41.1#!41.1" 41.1#!41.1"41.1"

11,500 /

41.1#!41.1"41.1"41/r

2olvin' this for rwe 'et r = 1.5%

)o 'et the forward rate for year 5, r5, the followin' euation (ay +e set up :

1,$50 1,$50 1,$50 100,100 = / /

41.1#! 41.1#!41.1" 41.1#!41.1"41.1"

1,$50 /

41.1#!41.1"41.1"41.15

11,$50 /

41.1#!41.1"41.1"41.1541/r5

2olvin' this for r5we 'et r5 = 15.08%

8!


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Chapter .s!

*o$ember December Manuary 'ebruary &arch April &ay Mune

1. 2ales 1#0 1#0 150 150 150 #00 #00 #00#. ?redit sales 8 8 105 105 105 10 10 10. ?ash sales ! ! 5 5 5 !0 !0 !0. ?ollection of receiva+les 4a 9revious (onth .! .! #.0

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