Chapter 7 Problem 12
a). Complete the spreadsheet below by estimating the project's annual after tax cash flow.
b). What is the investment's net present value at a discount rate of 10 percent?
c). What is the investment's internal rate of return?
d). How does the internal rate of return change if the discount rate equals 20 percent?
e). How does the internal rate of return change if the growth rate in EBIT is 8 percent instead of 3 percent?
| Facts and Assumptions |
|
| Equipment initial cost $ |
$ 350,000 |
| Depreciable life yrs. |
7 |
| Expected life yrs. |
10 |
| Salvage value $ |
$0 |
| Straight line depreciation |
|
| EBIT in year 1 |
28,000 |
| Tax rate |
38% |
| Growth rate in EBIT |
3% |
| Discount rate |
10% |
| Year |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
| Initial cost |
350,000 |
|
|
|
|
|
|
|
|
|
|
| Annual depreciation |
|
50,000 |
50,000 |
50,000 |
50,000 |
50,000 |
50,000 |
50,000 |
|
|
|
| EBIT |
|
28,000 |
28,840 |
29,705 |
30,596 |
31,514 |
32,460 |
33,433 |
34,436 |
35,470 |
36,534 |
Chapter 7 Problem 13
In many financial transactions, interest is computed and charged more than once a year. Interest on corporate bonds, for example, is usually payable every six months.
Consider a loan transaction in which interest is charged at the rate of 1 percent per month. Sometimes such a transaction is described as having an interest rate of 12 percent per annum. More precisely, this rate should be described as a nominal 12 percent per annum coumpounded monthly.
Clearly, it is desirable to recognize the difference between 1 percent per month compounded monthly and 12 percent per annum compounded annually. If $1,000 is borrowed with interest at 1 percent per month compounded monthly, the amount due in one year is:
F = $1,000(1.01)12 = $1,000(1.1268) = $1,126.80 This compares to F = $1,000(1+.12) =$1,120.00 for annual compounding.
Hence, the monthly compounding has the same effect on the year-end amount due as the charging of a rate of 12.68 percent compounded annually. 12.68 percent is referred to as the effective interest rate.
To generalize, if interest is compounded m times a year at an interest rate of r/m per compounding period. Then,
The nominal interest rate per annum, or the APR = m(r/m) = r.
The effective interest rate per annum,or the EAR = (1+r/m)m - 1.
Consider a $100,000, 30 year, fixed-rate, 9 percent, home mortgage requiring monthly payments.
a. The monthly interest rate on the mortgage is 9%/12 months = .75%. What is the APR on the mortgage?
b. What is the EAR on the mortgage?
c. The borrower's payment book will look something like the following. Complete the entries for the first 6 months.
d. After paying on this mortgage for 15 years, what will be the remaining principal outstanding?
|
Outstanding Balance Beginning of Month |
Monthly payment |
Interest due |
Principal payment |
Outstanding Balance End of Month |
| Date |
| 01-31 |
$100,000 |
|
|
|
|
| 02-28 |
|
|
|
|
|
| 03-31 |
|
|
|
|
|
| 04-30 |
|
|
|
|
|
| 05-31 |
|
|
|
|
|
| 06-30 |
|
|
|
|
|
e. Suppose after 15 years the borrower has the opportunity to refinance the remaining principal on the mortgage with a new 15-year mortgage carrying an interest rate of 7 1/8%. Refinancing will involve $250 in costs and "points" equal to 1.5 percent of the amount borrowed.
If the borrower plans to live in the house for 15 more years, does it make economic sense to refinance? Does your answer change if the borrower only intends to live in the house for 5 more years and will pay off any loans outstanding at that time? You may ignore taxes and may assume there are no prepayment penalties on either mortgage.
Chapter 7 Problem 14
A company is considering two alternative methods of producing a new product. The relevant data concerning the alternatives appear below:
|
Alternative |
Alternative |
|
I |
II |
| Initial investment |
$64,000 |
$120,000 |
| Annual receipts |
$50,000 |
$60,000 |
| Annual disbursements |
$20,000 |
$12,000 |
| Annual depreciation |
$16,000 |
$20,000 |
| Expected life |
4 yrs |
6 yrs |
| Salvage value |
0 |
0 |
At the end of the useful life of whatever equipment is chosen the product will be discontinued. The company's tax rate is 50 percent and the discount rate is 10 percent.
a. Calculate the net present value of each alternative.
b. Calculate the benefit cost ratio for each alternative.
c. Calculate the internal rate of return for each alternative.
d. If the company is not under capital rationing which alternative should be chosen? Why?
e. Again assuming no capital rationing, suppose the company plans to produce the product indefinitely rather than quit when the equipment wears out. Which alternative should the company select? Why?
f. If the company is experiencing severe capital rationing, and plans to terminate production when the equipment wears out, would any of your answers above change?
Chapter 7 Problem 15
You work for Mattel, a profitable toy manufacturer, and you are negotiating with Warner Brothers for the rights to manufacture and sell Harry Potter lunchboxes (you already sell related action figures).
Your marketing department estimates that you can sell $800 million worth of lunchboxes per year for 3 years, starting next year. At the end of year 3, you will liquidate the assets of the business.
Given the following information about this new product investment, identify the relevant cash flows, and calculate the investment's net present value, benefit-cost ratio, and internal rate of return. Make whatever assumptions you feel necessary and explain them briefly.
| ($ in thousands) |
|
|
|
| Marketing Research Costs, to date |
|
$ 20,000 |
|
|
| Initial cost of new equipment |
|
$ 300,000 |
|
|
| Licensing rights to use images (To be expensed for tax purposes at time 0) |
$ 350,000 |
|
|
| Expected life |
|
5 yrs |
|
|
| Salvage value |
|
0 |
|
|
| Depreciation method |
|
Straight-line over 5 years to 0 salvage value |
| Selling price of new equipment in 3 years* |
|
$ 130,000 |
|
|
| Incremental annual sales |
|
$ 800,000 |
|
|
| Incremental annual production costs |
|
$ 200,000 |
|
|
| Incremental annual selling |
|
|
|
|
| and administrative costs |
|
$ 80,000 |
|
|
| Current annual overhead costs |
|
$ 200,000 |
|
|
| Immediate advertising expenses for launch (To be expensed for tax purposes at tme 0) |
$ 190,000 |
|
|
| Tax rate |
|
40% |
|
|
| Working capital required, as a % of production costs |
|
7.50% |
(Needed at time 0.) |
| Minimum required rate of return |
|
10% |
|
|
The company must pay a 40% tax on the difference between the selling price and the asset's book value at time of sale.