1

Introduction to Managerial Finance

FINE 5200G, Winter 2015

Solution to Assignment #2 Question 1 (25%)

a) (15%)

• Status quo (3%):

79.3603.01.0

03.15.20 =

−

×=P

• Timber expansion (3%):

17.4406.012.0

06.15.20 =

−

×=P

• Retail expansion (8%):

• Dividends in the next four years (2%):

80.2)12.01(5.21 =+×=D

136.3)12.01(5.2 2

2 =+×=D

5123.3)12.01(5.2 3

3 =+×=D

9338.3)12.01(5.2 4

4 =+×=D

• The stock price in three years (3%):

89.4505.014.0

05.19338.34 =

−

×=P

• The stock price today (3%):

74.3614.1

8943.45

14.1

9338.3

14.1

5123.3

14.1

136.3

14.1

80.244320 =+

+++=P

Decision (1%): Strategy b) leads to the highest stock price, the best of the three alternatives. b) (5%)

• If the company continued on its current path, the stock would have returned exactly 10% a year over any future time period.

• If the company adopts the strategy you recommend in a), its stock price would rise to:

6032.5206.012.0

06.15.2 4

3 =

−

×=P

in three years.

• The expected return (IRR) over the three-year holding period is thus:

3

3

2

2

)1(

6032.5206.150.2

)1(

06.150.2

1

06.150.279.36

RRR +

+×+

+

×+

+

×=

and the solution is R = 19.46%, c) (5%)

• Your friend would’ve bought the stock for P0 = $44.17 as calculated in a) above.

• The stock price in 3 years is expected to be:

2

6032.5206.012.0

06.15.2 4

3 =

−

×=P

• The expected return (IRR) over the three-year holding period is thus:

3

3

2

2

)1(

6032.5206.150.2

)1(

06.150.2

1

06.150.217.44

RRR +

+×+

+

×+

+

×=

and the solution is R = 12% or exactly the required rate of return. Question 2 (20%)

a) (15%)

• Portfolio I is just Stock A, so its return in each state of the economy is already known:

State Prob. Return

1 0.15 0.00

2 0.30 0.05

3 0.40 0.10

4 0.15 0.20

o Its expected return (i.e., mean) is: 085.020.015.010.040.005.030.000.015.0 =×+×+×+×

o Its standard deviation is:

0594.0)085.02.0(15.0)085.01.0(4.0)085.005.0(30.0)085.00(15.0 2222=−×+−×+−×+−×

• Similarly, Portfolio V is just Stock B and its expected return and standard deviation, calculated in the same way, are 0.1325 and 0.1408, respectively.

• For Portfolios II-IV, we can proceed as follows: o For each portfolio (e.g., II), work out its return for each of the 4 states of the

world: � For example, Portfolio II’s return in State 1 is:

0.25×0.00 + 0.75×0.40 = 0.3 � The calculation in other states is similar.

o Given portfolio returns for all the states, we then calculate the portfolio’s expected return and standard deviation as before.

o The results are summarized below for each portfolio (5% for each of the three Portfolios):

� Portfolio II:

State Prob. Return

1 0.1 0.3

2 0.4 0.1625

3 0.4 0.1

4 0.1 0.05

Mean 0.14

St. dev 0.0649

� Portfolio III:

State Prob. Return

3

1 0.15 0.2

2 0.3 0.125

3 0.4 0.075

4 0.15 0.075

Mean 0.1088

St. dev 0.0442

� Portfolio IV:

State Prob. Return

1 0.15 0.1

2 0.3 0.0875

3 0.4 0.0875

4 0.15 0.1375

Mean 0.0969

St. dev 0.0176

• Summary for all five portfolios:

Weight in Stock A Return St. Dev Portfolio

0 0.1325 0.1408 I (Stock B)

0.25 0.1206 0.0920 II

0.5 0.1088 0.0442 III

0.75 0.0969 0.0176 IV

1 0.0850 0.0594 V (Stock A)

b) (5%)

• Portfolio V (or Stock A) is ruled out as a preferred choice because it is clearly dominated by both Portfolios III and IV: both portfolios have better expected returns and lower risk.

B

II

III

IV

A

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

Ex

pe

cte

d r

etu

rn

Stardard deviation

4

• For the remaining 4 portfolios (I-IV), there is no domination (i.e., no portfolio with the highest return and lowest risk). It’s a trade-off between risk and return.

• One way to make a choice is to apply the Sharpe ratio to evaluate the risk-return trade-off:

Weight in Stock A Return St. Dev Portfolio Sharpe

0 0.1325 0.1408 I (Stock B) 0.728

0.25 0.1206 0.0920 II 0.985

0.5 0.1088 0.0442 III 1.781

0.75 0.0969 0.0176 IV 3.795

1 0.0850 0.0594 V (Stock A) 0.926

The Sharpe ratio suggests that Portfolio IV provides the best trade-off between risk and return.

Question 3 (20%)

• Payback period calculation (5%):

Payback period calculation

Cash flow Payback period

Year Project A Project B

Project

A

Project

B

Project

A

Project

B

0 -110000 -110000

-110000 -110000

1 60000 10000

-50000 -100000

2 40000 20000

-10000 -80000

3 30000 30000

20000 -50000 2.33

4 10000 45000

30000 0

5 10000 80000

40000 80000

4.06

33.230000

100002 =+=APayback , 06.4

80000

50004 =+=BPayback

• NPV calculation (5%):

50.918211000012.1

5000

12.1

15000

12.1

30000

12.1

40000

12.1

600005432

=−++++=ANPV

32.1021811000012.1

80000

12.1

45000

12.1

30000

12.1

20000

12.1

100005432

=−++++=BNPV

• PI calculation (4%):

083.1110000

12.1

5000

12.1

15000

12.1

30000

12.1

40000

12.1

600005432

=

++++

=API

093.1110000

12.1

80000

12.1

45000

12.1

30000

12.1

20000

12.1

100005432

=

++++

=BPI

• IRR calculation (4%):

%73.160110000)1(

5000

)1(

15000

)1(

30000

)1(

40000

1

600005432

=⇒=−

+

+

+

+

+

+

+

+

+AIRR

RRRRR

%73.140110000)1(

80000

)1(

45000

)1(

30000

)1(

20000

1

100005432

=⇒=−

+

+

+

+

+

+

+

+

+BIRR

RRRRR

5

• Recommendation (2%): o From the above calculations, the payback and IRR methods support Project A while

the NPV and PI methods support Project B. o Whenever there are conflicting rankings, we should rely on the NPV criterion to

make decisions. So Project B should be chosen. Question 4 (35%) a) (25%)

• Operating CF projection: o Unit sale projections for the next three years are provided in the question. Beyond that, zero

growth in unit sales is expected. o Unit price, currently at $2.80, rises at 2% rate of inflation each year. o COGS – gross is projected using percentage of sales, i.e., it is 35.3/100.8 = 35.00% of sales.

� NOTE: You may project COGS using a different approach (i.e., other than percentage of sales), as long as you provide a reasonable rationale for them.

o Operating savings per unit are $0.031 in today’s dollars, which grows at the rate of inflation (2% per year): $0.031×1.02t ×units. � NOTE: The per unit savings apply to all frozen pizzas, from both current operations and

expansions. o Annual operating savings are $140,000 in today’s dollars, which grows at the rate of

inflation (2% per year): $140,000×1.02t. o CCAs are provided in the question. o Tax rate is 35%, given in the question.

0 1 2 3 4 5 6 7 8 9 10

Sales -units: 7.2 13.2 17.4 17.400 17.400 17.400 17.400 17.400 17.400 17.400

Unit price 2.856 2.913 2.971 3.031 3.091 3.153 3.216 3.281 3.346 3.413

Sales - total: 20.563 38.453 51.702 52.736 53.791 54.867 55.964 57.083 58.225 59.389

COGS - gross: 7.197 13.459 18.096 18.458 18.827 19.203 19.587 19.979 20.379 20.786

Savings-expansion: 0.228 0.426 0.572 0.584 0.596 0.607 0.620 0.632 0.645 0.658

Savings-current: 1.138 1.161 1.184 1.208 1.232 1.257 1.282 1.308 1.334 1.360

COGS - net: 5.831 11.872 16.339 16.666 16.999 17.339 17.686 18.040 18.400 18.768

Oper. Exp. - gross: 11.310 21.149 28.436 29.005 29.585 30.177 30.780 31.396 32.024 32.664

Ann. Savings: 0.143 0.146 0.149 0.152 0.155 0.158 0.161 0.164 0.167 0.171

Oper. Exp. - net: 11.167 21.004 28.288 28.853 29.430 30.019 30.619 31.232 31.856 32.494

CCA: 1.377 2.436 1.881 1.464 1.146 0.909 0.484 0.588 0.483 5.493

EBIT 2.188 3.142 5.194 5.753 6.215 6.600 7.175 7.224 7.485 2.635

Taxes: 0.766 1.100 1.818 2.014 2.175 2.310 2.511 2.528 2.620 0.922

NI: 1.422 2.042 3.376 3.739 4.040 4.290 4.664 4.696 4.865 1.712

Operating CF: 2.799 4.478 5.257 5.203 5.186 5.199 5.148 5.284 5.348 7.205

• Additions to net working capital (NWC) in the project: o Accounts receivables, inventory and accounts payable are all projected using % sales.

6

o From last year’s balance sheet, these three items are 12.1/100.8 = 12.00%, 7.1/100.8 = 7.00%, and 8.1/100.8 = 8.00% of sales.

o Combining with the sales projections above (from the expansion project, not the firm as a whole), we have the projections for accounts receivables, inventory and accounts payable.

o Additions to NWC is the just the increase in NWC each year. o The total amount of the NWC in the final year ($1.404 million) is recovered at the end of

that year.

NWC projection 1 2 3 4 5 6 7 8 9 10

Accounts receivables 2.468 4.614 6.204 6.328 6.455 6.584 6.716 6.850 6.987 7.127

Inventory 1.439 2.692 3.619 3.692 3.765 3.841 3.917 3.996 4.076 4.157

Accounts payable 1.645 3.076 4.136 4.219 4.303 4.389 4.477 4.567 4.658 4.751

NWC 0.750 2.262 4.230 5.687 5.801 5.917 6.035 6.156 6.279 6.405 6.533 Sum

Additions to NWC 0.750 1.512 1.968 1.457 0.114 0.116 0.118 0.121 0.123 0.126 0.128 6.533

• Total cash flow and NPV calculation:

0 1 2 3 4 5 6 7 8 9 10

Operating CF: 2.799 4.478 5.257 5.203 5.186 5.199 5.148 5.284 5.348 7.205

Additions to NWC -0.750 -1.512 -1.968 -1.457 -0.114 -0.116 -0.118 -0.121 -0.123 -0.126 -0.128

NWC recovery: 6.533

Initial capital: -16.500

Salvage value: 0

Total CF: -17.250 1.287 2.510 3.800 5.090 5.070 5.080 5.027 5.160 5.223 13.610

NPV: 4.319

So, the NPV of the proposed expansion project is $4.319 million:

319.415.1

610.13

15.1

223.5

15.1

160.5

15.1

027.5

15.1

080.5

15.1

070.5

15.1

090.5

15.1

800.3

15.1

510.2

15.1

287.125.17

1098765432=++++++++++−

Approve the project. b) (5%)

• Cost of equity: 1026.005.02.10206.0 =×+

• WACC: 0825.06.01026.04.0)35.01(0706.0 =×+×−×

c) (5%)

• Recalculate NPV using WACC = 8.25% as the hurdle rate (keeping everything else the same as before):

694.130825.1

610.13

0825.1

223.5

0825.1

160.5

0825.1

027.5

0825.1

080.5

0825.1

070.5

0825.1

090.5

0825.1

800.3

0825.1

510.2

0825.1

287.125.17

1098

765432

=+++

+++++++−

M

7

• With either hurdle rate, the NPV is positive. o The question is then how high must the hurdle rate go before the NPV is reduced to

zero? To answer that question, we calculate the IRR of the project::

0)1(

610.13

)1(

223.5

)1(

160.5

)1(

027.5

)1(

080.5

)1(

070.5

)1(

090.5

)1(

800.3

)1(

510.2

1

287.125.17

1098765432=

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+−

RRRRRRRRRR

and we find that IRR = 19.71%. So as long as the hurdle rate is less than 19.71%, we should accept the project. As it is quite unlikely for the hurdle rate to rise from the current WACC of 8.25% to 19.71%, the expansion project is most likely a positive NPV project. Accept the project.