first, convert all of these into effective annual rates, and then convert real to nominal or nominal to real to make the comparison. I'll convert real to nominal.
so, the 7% nominal, compounded semi-annually is a slightly better deal.
Lundquist College of Business
Finance 316, Spring 2000
Midterm Answer Guide
Prof. Jarrad Harford
1. You are considering two investment options. The first offers you a 4% real return, compounded annually. The second offers you a 7% nominal return, compounded semi-annually. If you expect inflation to be 3%, compounded annually, which one should you go with? [6]
first, convert all of these into effective annual rates, and then convert real to nominal or nominal to real to make the comparison. I'll convert real to nominal.
so, the 7% nominal, compounded semi-annually is a slightly better deal.
2. If depreciation isn't a cash flow, why do we care about it in capital budgeting? [5]
Depreciation may not me a cash flow, but it reduces net income, so it affects taxes, which are cash flows. Capital budgeting is concerned with anything that affects cash flows, so we have to pay attention to depreciation charges.
3. You are looking at purchasing a house. The house will cost $150,000 and you are going to put 20% ($30,000) down, meaning that you will have to borrow $120,000. Assume mortgage rates are 8.4% (compounded monthly). You can get a 30-year fixed rate mortgage with your first payment due one month after you buy the house.
a. What will your monthly payments be? [6]
This is a straight-up annuity, which can be seen from the cash flow timeline:
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | … | 359 | 360 |
| CF | CF | CF | CF | CF | CF | … | CF | CF |
the present value is the amount you are borrowing. In return, you are giving the bank an stream of equal payments at regular intervals (an annuity) with a present value equal to the amount they are giving you (the loan amount).
b. You can also get a 15-year mortgage with a $40,000 balloon payment at the end (your 180th payment will be $40,000). What will your monthly payments be for the first 179 months of this mortgage? [7]
You can do this one just like we did the car lease in class (remember that I said a
lease is just like a loan with a balloon payment at the end). It's important to use a
timeline for this one:
| 0 | 1 | 2 | 3 | 4 | 5 | 6… | 178 | 179 | 180 |
| CF | CF | CF | CF | CF | CF… | CF | CF | 40,000 |
so, the part you have to cover with your regular payments is the difference between what you're borrowing ($120,000) and the present value of the balloon payment:
so your regular payments are just a bit higher, but you pay it off in half the time (with a big payment at the end).
4. Evaluate the following statement: "Financial managers should maximize earnings (profits)." Explain your reasoning. [6]5. The following table contains STRIP prices and spot rates for various maturities. All spot rates are quoted as APR's, semi-annually compounded.
| Time | 6 months | 1 yr | 1.5 yrs | 2 yrs | 2.5 yrs | 3 yrs |
| STRIP Price | 96:20 | 93:08 | 90:00 | 86:28 | 83:27 | 80:30 |
| Spot Rate | 0.07 | 0.071 | 0.0714 | 0.0716 | 0.0717 | 0.0717 |
a. Use either the spot rates or STRIP prices to price a 2-year government bond with 6% coupons, paid semi-annually. Assume the first coupon is due six months from today. (Note: you will not get exactly the same price if you do it both ways to check your answer because of rounding in the STRIP prices). [5]
For an example of how to do it using the spot rates, see quiz #2. When using the STRIP prices, remember that the 2 digits after the colon are 32nds of a dollar and must be converted to cents by dividing by 32. You can think of STRIP prices as telling us what the PV of a $100 received at a future date is. Thus, we can convert them to the PV of a dollar by dividing by 100. The price of a bond is the sum of the present values of the cash flows in the bond. The cash flows in this bond look like this (remember, semi-annual payments means half the coupon amount is received every 6months):
| 6 mos | 1 yr | 1.5 yr | 2 yrs |
| 30 | 30 | 30 | 1030 |
30(.90625)+30(.9325)+30(.9000)+1030(.86875)=978.78
b. Approximately what is the YTM for this bond? (You do not have to calculate the YTM.) Explain. [4]
The yield-to-maturity for this bond is a little bit less than 7.16%. Recall the YTM can be thought of as a complicated weighted average of the spot rates going into the pricing of the bond where the weights are approximately proportional to the sizes of the cash flows. Thus, the YTM must lie between 7% and 7.16% and since the biggest cash flow by far is the 1030, most of the weight will be on the 7.16%, pulling the average very close to it.
c. If the STRIP prices decrease, will the YTM for this bond increase or decrease? Explain. [4]
If STRIP prices decrease, that means that spot rates have increased (STRIPs are just bonds and bond prices and interest rates move in the opposite direction). The only way STRIP prices would go down is if spot rates have increased, and since YTM is an average of spot rates, YTM must increase as well.
d. If you think interest rates are going to go up, is it a good time to buy bonds? Explain. [4]
No. It is a bad time to buy bonds. If we think interest rates are going to go up, then we think bond prices are going to go down, so we'll be buying high and selling low--not the road to success.
6. What is a sunk cost and why should it be ignored? What is an opportunity cost and why should it be included in capital budgeting analysis? [10]
A sunk cost is a cost that has already been spent or committed. Since it has already been spent, it is not incremental to the project. If you ask is this cash flow different with the project than without it, the answer is no: with the project, we have spent it, without the project, we have still spent it. We only consider incremental cash flows in capital budgeting.
An opportunity cost is something that we give-up by taking a project. For example, if we own a piece of land and use it in our project, the land is not free just because we already own it. By using it in the project, we give up the opportunity to sell it. So the opportunity cost for this project is the market value of the land. With the project, we can't sell the land. Without the project, we can sell the land. Since the opportunities are different with vs. without the project, it is very relevant.
7. You are planning for your retirement. You plan to invest $200 every month for 40 years.
a. If you invest your first $200 immediately and make 480 more investments, how much will you have in your retirement account at the end? Assume an interest rate of 12%, compounded monthly. [6]
This question is asking for the future value of an annuity. As usual, we'll break it down into 2 things we know how to do: the present value of an annuity and the future value of a present value:
b.When you retire, you plan to make withdrawals every month for 20 years. You will be investing more conservatively in your old age and earning a nominal rate of only 9%, compounded monthly. You expect inflation to be 3.6% per year, compounded monthly. You want to withdraw an amount that stays constant in real dollars. If your first withdrawal is one month after you stop investing, what constant real amount can you withdraw? If you are having trouble with handling the real part of this problem, you can find the constant nominal amount and receive 2 points off. [7]
First, compute the monthly real rate of interest by dividing 1 plus the monthly nominal rate by 1 plus the monthly inflation rate: monthly nominal=.09/12=.0075 and monthly inflation= .036/12=.003, so monthly real is (1.0075/1.003) -1 =.004487. Now, just compute the annuity payments using the monthly real rate and 240 months (20 years):
8. What does the NPV tell us? What is the NPV decision rule? How does it help us meet our goal as financial managers? [10]
NPV tells us the dollar value of an investment's affect on the value of the firm's assets. Since the wealth of the shareholders come from the value of the firm's assets, NPV measures the dollar value effect of an investment on shareholder wealth. Since our objective is to maximize shareholder wealth, a measure that tells us the actual effect of an investment on that wealth is the perfect decision tool. We accept projects that increase shareholder wealth and reject those that don't.
9. You have just completed a $1 million test-marketing program for the Gizmo. The results of the test-marketing indicate that the Gizmo will sell well. Therefore, you estimate that over the 5 years you plan to sell the Gizmo, it will have revenues of $100 million per year. It will also generate costs of $90 million per year.
Production will require you to purchase $20 million worth of equipment, which will be depreciated to 0 using straight-line depreciation over 5 years. The new equipment can be sold for $1.5 million at the end of the project. You will also need to use existing equipment which is fully depreciated, but could be sold right now for $1 million (the existing equipment will be worthless at the end of this project).
Working capital will have to increase immediately to $10 million from its current level of $8 million. It will increase again in year 3 to $11 million and will decrease back to $8 million in year 5. The project will produce 10% of the firm's revenues for the next 5 years and 10% of current overhead is $500,000 per year.
Your tax rate is 34% and your cost of capital for this project is 12%. Calculate the NPV of this project. [20]
The $1 million on test marketing is sunk. We have spent it whether we take the project or not, so it is an irrelevant cash flow. The last sentence of the 3rd paragraph (about the firm's current overhead is irrelevant). Current overhead is existing overhead that should not be allocated to a new project because we'll have that overhead whether we take the project or not. Working capital levels look like this:
| 0 | 1 | 2 | 3 | 4 | 5 |
| 10 | 10 | 10 | 11 | 11 | 8 |
changes required to reach those levels are:
| 0 | 1 | 2 | 3 | 4 | 5 |
| +2 | 0 | 0 | +1 | 0 | -3 |
since it costs money to increase working capital and we get that money back when we decrease it, cash flows from these changes are equal, but in the opposite direction:
| 0 | 1 | 2 | 3 | 4 | 5 |
| -2 | 0 | 0 | -1 | 0 | +3 |
The fact that the existing equipment could be sold right now for $1 million is important. If we take the project, we have to use it and can't sell it, so its market value represents an opportunity cost equal to the after tax cash-flow from selling it. It is fully depreciated so its book value is zero and the whole $1 million would be taxed as profit, leaving us with $1M- [$1M(.34)]=$0.66M in after tax cash flow that we are giving up if we take this project. This is a cost.
The new equipment will cause a $20M outflow immediately when we purchase it and create $4M depreciation charges per year (straight line depreciation to zero over 5 years: 20/5=4). We will sell it for $1.5M at the end of the project. Since its book value will have reached zero by then, the entire 1.5M will be taxed as profit and we will be left with 1.5-[1.5(.66)]=.99 after tax.
Now to the cash flows:
| 0 | 1 | 2 | 3 | 4 | 5 | |
| Rev | 100 | 100 | 100 | 100 | 100 | |
| -Costs | 90 | 90 | 90 | 90 | 90 | |
| -Depr | 4 | 4 | 4 | 4 | 4 | |
| =Op Inc | 6 | 6 | 6 | 6 | 6 | |
| -Tax @ 34% | 2.04 | 2.04 | 2.04 | 2.04 | 2.04 | |
| =AT Income | 3.96 | 3.96 | 3.96 | 3.96 | 3.96 | |
| +Add Back Depr | 4 | 4 | 4 | 4 | 4 | |
| =AT Op CF | 7.96 | 7.96 | 7.96 | 7.96 | 7.96 | |
| +Cap Inv | -20 | +0.99 | ||||
| +Opport Cost | -0.66 | |||||
| +CF from Chg in WC | -2 | 0 | 0 | -1 | 0 | +3 |
| =FCF | -22.66 | 7.96 | 7.96 | 6.96 | 7.96 | 11.95 |
The final step is to compute the NPV at a discount rate of 12% (your opp. cost of capital):
