MGT 326 Fall 2015 Test 1 Problem Solutions

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7. Your company is considering borrowing $4,000,000 at a cost of debt of 5.2600 p.a. If your company pays $220,000 each quarter towards this debt, how many years will it take to pay off the loan?

Solution Opt 1: rper = rnom/m = 5.26%/m = 1.315P/Y=1, I/Y=1.315, PV=-4000000, PMT=220000: CPT, N; N = 20.915; yrs = 20.915/4 = 5.23 yrsSolution Option 2:P/Y=4, I/Y=5.26, PV=-4000000, PMT=220000: CPT, N; N = 20.915; yrs = 20.915/4 = 5.23 yrs

8. You are considering two different stock mutual funds in which to invest. Fund A offers 8.5100% p.a. rate of return with monthly reinvestment of profits. Fund B offers a 8.5600% p.a. rate of return with quarterly reinvestment of profits. Compute the Effective Annual Rate for each fund. Which fund is more profitable?

Fund A: 2nd, INCONV, 8.51%, ENTER, ↓, ↓, 12, ENTER, ↓, ↓, CPT: 8.8500%Fund B: 2nd, INCONV, 8.56%, ENTER, ↓, ↓, 4, ENTER, ↓, ↓, CPT: 8.8387%

9. You are considering buying a new car which cost $22,999. You do not have that kind of cash so you must borrow the money. Your bank offers a nominal rate of 3.1200% for a 6 year amortized loan with monthly payments. You cannot afford to pay more than $320 per month. If you borrow the money from your bank, can you afford this car?n = T x m = 6 x 12 = 72Solution Opt 1: Find the PMTrperiodic = rnominal/m = 3.12%/12 = 0.26%; P/Y=1, N=72, I/Y=0.26, PV=22999; CPT PMT: $350.68 No

ORP/Y=12, N=72, I/Y=3.12, PV=22999; CPT PMT: $350.68 No

Solution Option 2: Find the PV @ PMT of $320P/Y=1, N=72, I/Y=0.26, PMT=320; CPT PV: $20,987.16 No

ORP/Y=12, N=72, I/Y=3.12, PMT=320; CPT PV: $20,987.16 No

Solution Option 3: Find I/Y @ PMT:$320 & PV:$22,999P/Y=12, N=72, PV=-22999, PMT:320; CPT I/Y: 5.8575% No

10. You are considering leasing a car that cost $35,999. The lease will be for 6 years and requires monthly payments of $300.00. Somewhere on the lease paperwork you notice a statement to the affect that you will be charged an APR of 3.1800%. What kind of annuity is this?___________________ What is the implied value of the car at end of the lease (i.e. what is its turn-in value)?Annuity DueSolution Opt 1:rperiodic = rnominal/m = 3.18%/12 = 0.265%;Set BGN, P/Y=1, N=72, I/Y=0.265, PV=35999, PMT= -300; CPT FV: $19,729.03Solution Option 2:Set BGN, P/Y=12, N=72, I/Y=3.18, PV=35999, PMT= -300; CPT FV: $19,729.03

11. What is the future value of an annuity due yielding 9.6400% APR that pays quarterly payments of $1,000 for 1 year? (Do the math; do not use the financial functions on your calculator. Draw a cash flow diagram)

FV = PV(1 + r/m)n + FV(1 + r/m)n-1 + ………….. = 1000(1 + 0.0964/4)4 + 1000(1 + 0.0964/4)3 + 1000(1 + 0.0964/4)2+ 1000(1 + 0.0964/4)1

= 1000(1.0241)4 + 1000(1.0241)3 + 1000(1.0241)2+ 1000(1.0241)1

= 1000(1.0999) + 1000(1.0741) + 1000(1.0488)+ 1000(1.0241) = 1,099.9412 + 1,074.0564 + 1,048.8000 + 1,024.1000 = $4,246.89

1 2 70 71 72

PMT = ?

PV = $26,999

5 yrs

0

1 2 70 71 72

PMT = $300.00

PV = $35,999

6 yrs

m=12, T=6; n = m x T = 12 x 6 = 72

0

Turn-in Value = ?

PMT = $1,000

1 2 3

FV = ?

0

MGT 326 Fall 2015 Test 1 Problem Solutions

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12. Today you open a new investment account for your company with a $12,000 deposit. The account has had an average yield of 8.2400% over the last four years and compounds every quarter. You plan to deposit $12,000 into this account every month at the beginning of the month. How much will you have in this account 4.5 years from now?

Set BGN, P/Y=12, C/Y=4, N=54 I/Y=8.24, PMT=12000; CPT,FV: FV =$785,570.47  OR

Convert the weekly rate into a quarterly rate then solve for FV2nd , ICONV, 8.24, ENTER, ↓, 4, ENTER, ↓, ↓, CPT: EFF% = 8.4981%

,↓12 ,ENTER. ↓, CPT: NOM% = 8.1841%Set BGN, P/Y=12, N=54, I/Y=8.1841, PMT=12000; CPT,FV: FV = $785,570.47

13. You are tasked with estimating the fair market value of a security that promises uneven future payments. The table below shows the quarterly payment schedule (each cash flow occurs at the end of the quarter). You consider 8.2000% APR to be the appropriate opportunity cost of capital. What is the theoretical value of this security?

1 2 52 53 54 mos

PMT = $12,000

FV = ?

0

1 2 3 4 5 6

550 650 820 -750 300 400

I/Y = rperiodic = rnominal/m = 12.4%/4 = 3.01%CF, 2nd, CLR WORK (Clear Cash Flow Registers)0, ENTER, ↓, 550, ENTER↓, ↓, 650, ENTER↓, ↓, 820, ENTER↓, ↓, -750, ENTER↓, ↓, 300, ENTER↓, ↓, 400 ENTERNPV, 3.01, ENTER↓, CPT = $1,819.99

14. Your company plans to sell the security described in Problem 13 (above). What would the rate of return for your company be if the sales price is $1,950.00? ROR = (SP-FMV) / FMV = ($1,950 - $1,819.99 ) / $1,819.99 = 0.071433 = 7.1433%

15. You plan to retire on your 65th birthday. After that time, you want to withdraw $8,500.00 each month at the beginning of the month for the rest of your life. How much money must you deposit monthly into a retirement account starting on your 22nd birthday to fund the above described retirement plan? You will make these deposits at the beginning of each month. You estimate the average rate of return over the rest of your life will be 8.2000% p.a. [Hint: Treat the retirement cash flows as a perpetuity.]

Step 1: Find the PV of the retirement perpetuity. PV = PMT/rperiodic = $8,500/(0.082/12) = $1,243,902.44

Step 2: Find the PMT of the retirement savings annuity. Find PMT: Set BGN, P/Y=12, N=43x12=516, I/Y=8.2, FV=1,243,902.44; CPT,PMT: $259.11