FIN 350 Midterm Harford WINTER 2019

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University of Washington *

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350

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Finance

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Apr 3, 2024

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Assume inflation is 2.4% APR, NAME__W19 ANSWER KEY ____ compounded monthly 1 of 5 1. You are choosing between two loans. One charges a real interest rate of 7.3% APR, compounded annually. The other charges a nominal rate of 9.8% APR, compounded semi annually. Which has the lower rate? [6] You need to get these both on equal footing. The easiest is to convert them both into nominal EAR’s. Since the real rate is annual, you need to convert the inflation rate to annual as well. It is given as 2.4% APR, compounded monthly, which is 0.002% per month, so its annual equivalent is (1+(.002)) 12 -1=0.024266. Thus, the annual nominal rate to go with the 7.3% real rate is (1.073)(1.024266)-1=0.0990 The other rate is already a nominal rate, but needs to be converted into an EAR: (1+(.098/2)) 2 -1=.1004 Thus, the real rate is lower. 2. A company makes the following offer: give us ten payments of $100, and then we’ll give you $100 per year forever! Assume that you make the first payment immediately and then make 9 more at annual intervals. One year after your last payment, they start paying you (this would be year 10). If your opportunity cost of capital is 10%, should you accept this deal? [8] You have to compare the PV of what you give to the PV of what you get. What you give is just an annuity due. What you get is a deferred perpetuity. What you give: 𝑷𝑽 ൌ 𝟏𝟎𝟎 ൅ 𝟏𝟎𝟎 . 𝟏𝟎 ቂ𝟏 െ 𝟏 ሺ𝟏 . 𝟏𝟎ሻ 𝟗 =675.90 What you get: the value of the perpetuity in the year before it starts is 100/.10 = 1000. Since it starts in year 10, that means that its value in year 9 is 1000. Its value today is: 𝑷𝑽 ൌ 𝟏𝟎𝟎𝟎 ሺ𝟏 . 𝟏𝟎ሻ 𝟗 ൌ 𝟒𝟐𝟒 . 𝟏𝟎 Pretty crazy, but it’s a bad deal! The value of the perpetuity is less than what you pay to the company because it is deferred. 3. Let’s say you put $100 in an account earning 6% APR, compounded monthly. How long will it take for the $100 to grow to $500? [4] 6% APR, compounded monthly is .06/12 = 0.005 per month. 500 ln ln 100 322.69months ln 1 .005 ln 1 .005 FV PV n
Assume inflation is 2.4% APR, NAME__W19 ANSWER KEY ____ compounded monthly 2 of 5 4. Assume the following term structure of risk free interest rates: 6 months 1 year 1.5 years 2 years 2.5 years 1.4% 1.3% 1.2% 1.1% 1.0% **All rates are quoted as semi annually compounded APR’s.** a. Which would have the higher yield to maturity: a 2.5 year STRIP or a 2.5 year 4% coupon Treasury bond? Explain. [6] The STRIP only has one cash flow, so its YTM is simply the rate for that maturity: 1%. The coupon bond has cash flows every 6 months, so it puts weight on all 5 rates. Since all of the other rates are higher than 1%, the coupon bond will have the higher yield to maturity. b. If 1.5 year corporate zero coupon bonds ($1000 par) with BBB rating have credit spreads of 320 basis points, what would be the price of such a bond? [5] 320 bp is 3.20%. Adding the spread to the Treasury rate of 1.2% gets us to 4.4%: 𝑃𝑉 ൌ 𝐹𝑉 1 ൅ 𝑟ሻ 1000 1 . 044 2 936.80 c. If you think the BBB rated bonds have a 20% chance of default (payoff=$800), and an 80% chance of paying as promised, what is your expected return from buying the 1.5 year zero coupon bond in part (b)? [6] Expected CF = (.20)(800)+(.80)(1000) = $960 𝑟 ൌ ൬ 960.00 936.80 1 0.00818 0.818% 0.818% x 2 = 1.64% APR
Assume inflation is 2.4% APR, NAME__W19 ANSWER KEY ____ compounded monthly 3 of 5 5. How are IRR and NPV related and how are they different? [6] IRR and NPV are based on the same cash flow equation. NPV takes the cash flows and discounts them using the opportunity cost of capital. IRR takes the cash flows and finds the discount rate that creates a zero NPV. NPV gives you the dollar value impact of a project on the firm. Loosely speaking, IRR tells you the annualized average return you would get from taking the project. Thus, both try to tell you the impact of the project, but one does it in terms of value impact and the other does it in terms of return. 6. You have to buy a new copier. The cost of the copier is $2000 now, plus $400 per year in maintenance costs. The copier will last for 5 years. Alternatively, a local company offers to lease the copier to you and do the maintenance as well. If your discount rate is 6% per year, what is the most you would be willing to pay per year to lease the copier (your first lease payment is due in one year)? [8] This is basically an EAC question. You need to know what the EAC of buying the copier is, so you know the maximum annual cost (lease) you would be willing to pay. First get the total PV of owning the copier and then figure the EAC based on that PV: 0 1 2… 5 2000 400 400… 400 5 5 1 1 $2000 $400 $3684.95 .06 .06 1 .06 3684.95 $874.79 1 1 .06 .06 1 .06 PV EAC So 874.79 is the maximum lease payment you would be willing to make. 7. If you plan to hold a coupon bond until maturity, you know it will be worth exactly $1000 at the end (when it repays par value). Why would you ever buy a coupon bond selling at a premium? [6] It doesn’t matter whether a bond is selling at a premium, par or discount. The price it sells at is the price required so that if you pay that price and receive the cash flows from the bond, you will receive a rate of return that is the going fair market return at that point in time. In premium bonds, you receive above average income return (current yield), but you suffer a capital loss when the bond eventually returns to $1000 par value at maturity. These offset to give you a fair total return.
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