Name:______
First Midterm Exam
MBAC 6060
Fall 2006
This exam will serve as the answer sheet. You should have enough room; however, if you require more space in which to write your answers I have additional paper at the front. There are 5 full problems (some with multiple parts) on this exam; be sure you are aware of them all. If you would like to have the possibility of partial credit for any of the questions, be sure to show how you developed the answers rather than simply reporting a numerical answer. You have an hour and a half for this exam. Assume all interest rates are given on a stated annual basis and that compounding is done annually unless otherwise explicitly stated for a given problem.
(1) (10 points) You are able to borrow or lend from your bank at a rate of 9%.
(a) What is a promise of receiving $3,250 in two years worth to you today?
$3,250/(1.09)2 = $2,735.46
(b) What is a promise of receiving $6,375 in twelve years worth to you today?
$6,375/(1.09)12 = $2,266.53
(c) Explain why these are the answers to (a) and (b).
Simply because this is the amount you would need to put in the bank at 6% in order to generate the stated amounts at the stated points in time. For example, if you put $186.36 in the bank today you would receive $375 in twelve years; thus, receiving $375 in twelve years must have a present value of $186.36.
(d) What are the answers to parts (a) and (b) if compounding is done monthly on comparable alternative investments?
$3,250/(1.0075)24 = $2,716.45 and $6,375/(1.0075)144 = $2,173.66
(2) (15 points) You are considering an opportunity to buy a perpetuity as part of your retirement plans. Currently the stated annual interest rate is 7% and compounding is done semi-annually in the financial markets. The perpetuity that has caught your eye makes payments of $1 every two years where the first payment occurs in five years. What is a fair price for the perpetuity?
There are a few issues with this problem. First we have to find the effective rate of interest to use to discount the cash flows of the perpetuity. With a 7% stated annual rate with compounding every ½ year this means the effective annual rate is (1.07/2)2 = 1.071225 or 7.1225%. Now the perpetuity has cash flows that come every two years so we also need an effective two year rate to value this stream of cash flows. This is (1.071225)2 = 1.147523 or 14.7523%. Using the perpetuity formula we see that the value of the perpetuity is $C/r = $1/.147523 = $6.78. This value is as of one period before the first cash flow for the perpetuity. A period for this perpetuity is two years. Thus this value is as of 3 years from now. We need to discount this value back 3 years to find a present value. We do this using the effective annual rate: $6.78/(1.071225)3 = $5.52. This is what you should be willing to pay (you would always be willing to pay less but competition in the market should not allow you to find such a bargain).
(3) (25 points) Debt pricing.
(a) You learn on Yahoo Finance the following information concerning the current spot rates:
Maturity / Spot Rate6 months / 6.0%
1 year / 6.2%
18 months / 6.3%
2 years / 6.6%
30 months / 6.8%
3 years / 7.0%
42 months / 7.1%
You are asked to estimate the current price for a standard coupon bond that has 2 ½ years to maturity, a 5% coupon interest rate, and a $1,000 face value, for which the next coupon will be received in 6 months. What is that estimate?
(b) Given the price you calculated in part (a) and the characteristics of the bond described, what is its yield to maturity?
(4) (25 points) The formula for free cash flow appears below.
Net Income
This is the starting point that captures the value (in accounting terms) generated (or if it is a forecast expected to be generated) for a given period by the firm in question.
+Depreciation
This is short hand for adding back non cash expenses. Net income has non-cash expenses taken out and since they do not represent actual cash flows for the period in question we add them back so that we can capture cash flow.
+ Change in deferred income tax liabilities (long term)
This is simply an adjustment for accruals dealing with taxes. In conjunction with some of the pieces of changes in net working capital this converts “allowance for income taxes” to actual (cash) taxes paid.
- Changes in Net Working Capital (“sort of”)
This adjustment accomplishes two things, there are adjustments for accruals (i.e. changes in accounts receivable and accounts payable, etc.) to change booked revenues and expenses to a cash basis. It also adjusts for changes in investments in short term assets the firm needs to operate effectively (i.e. cash, inventory, etc.).
- Net Capital Expenditures
This adjusts net income for cash payouts and receipts that do not appear directly on the income statement and account for how the firm invests in long term assets.
+ After-tax Interest
This accomplishes two things. First it puts interest back into net income (if the firm uses debt and so pays interest it was taken out) which is cash that the firm has generated and was certainly available to be paid to a contributor of capital (as it in fact was) so it belongs as part of what we call free cash flow. Secondly it adjusts the taxes actually paid by the company to taxes that an all equity firm would have paid.
First define free cash flow and then provide an explanation for each of the elements in the formula.
(5) (25 points) Pricing Equity
(a) Zender Inc paid its annual dividend yesterday in the amount of $10,000 per share (owing solely to a very generous CEO). This dividend is expected to remain constant for the foreseeable future. The appropriate discount rate for an investment in this stock is 5%. What is the current price per share of Zender stock? What will its price be in 4 years?
We first use a perpetuity formula to value the equity today: $10,000/0.05 = $200,000 per share a true testament to the market’s ability to discern value. Then we note that in 4 years we will be in exactly the same situation and so the price will be $200,000 per share at that time as well.
(b) Ahlburg Inc. will pay its annual dividend tomorrow in the amount of $1.25 per share. Dividends for Ahlburg Inc. are expected to grow at a constant rate of 2% per year forever and the market has determined that a discount rate of 12% is appropriate for the company’s stock. What is today’s price per share of Ahlburg stock? What will the price of Ahlburg stock be in 4 years?
Today we value the stock as a growing perpetuity where the payment received in a year is $1.25(1.02) = $1.275 so the value of the dividends from time 1 onward is $1.275/(0.12 – 0.02) = $12.75. To this we must add the $1.25 we will receive tomorrow so the price per share should be $14.00 today. In four years we still have a perpetuity growing at 2% but the dividend received in four years and a day is $1.353 and the dividend to be received at time five will be $1.3801 so the value per share in 4 years will be $1.353 + $1.3801/0.10 = $15.15.
(c) Why did the price change (between the current price and the price in 4 years) in part (b) but did not in part (a) (this will take some thought)?
The problem stated that for Zender stock investors want a return of 5% per year. If you invest the $200,000 to buy a share the $10,000 in dividends you will receive will provide you with exactly a 5% return. Thus no capital gain is necessary. For Ahlburg stock note that the same is not true, the dividend yield is not sufficient so that you receive the required 12% return for holding this stock and thus there must be some capital gain (i.e. a price increase each period) included in your return stream as well as the dividend yield (in reality this would all be on an expected basis as we don’t know the future with certainty).