Final SUMMER 2018

Problem 1 1. (5 points) Suppose that you are advising a couple just about to get married about how much they need to save for college for their future child. They plan on having one child, who will be born in 10 years. This child will start college 18 years after being born. You estimate the child’s annual cost of education will be $100,000 per year, payable at the beginning of the school year. We assume four years of college expenses for the child. The effective annual interest rate is 8%. When you ask the couple how they plan to save for the necessary college funds, they tell you that they want to make a single deposit of $Z in 7 years. The total of this deposit will be exactly enough to cover the child’s college expenses. Find Z.

𝐹𝑢𝑡𝑢𝑟𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 7 𝑦𝑒𝑎𝑟𝑠=41,463.45∗ 1+8% 7 =71,061.07 Problem 1 Answer: P𝑉 𝑜𝑓 𝑐𝑜𝑠𝑡= 100,000 1+8% 28 + 100,000 1+8% 29 + 100,000 1+8% 30 + 100,000 1+8% 31 =41,463.45， 𝐹𝑢𝑡𝑢𝑟𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 7 𝑦𝑒𝑎𝑟𝑠=41,463.45∗ 1+8% 7 =71,061.07

Problem 2 2. Alright Is All Left, Inc. stock is currently valued at $60 per share. One year from today, the stock’s value could be (in increasing order) $40, $X, $Y, each with one-third probability. Janet can buy a European call option with an expiration date one year from today. This option has a present value of $4, and has a one-third probability of having a positive value on the expiration date. The exercise price for this option is $75. The effective annual discount rate for this option is 20%.

Problem 2 (a) (4 points) Can you determine exactly what X can be? Why/why not? If you can determine X, calculate its exact value. If can only determine a range that X can be, determine what that range can be. Answer: As 40<X<Y, the option will be “in the money” only if Y is the outcome. X must be between $40 and $75. We cannot pinpoint X any more, since there is no more information to help determine the exact value.

Problem 2 (b) (4 points) Can you determine exactly what Y can be? Why/why not? If you can determine Y, calculate its exact value. If can only determine a range that Y can be, determine what that range can be. Answer: Y>75, since this is the only value that is “in the money”. Since the value of option is known, we can find Y exactly. 4= 1 3 𝑌−75 1+20% , 𝑌=89.40

Problem 3 (7 points; You may find this to be a challenging question.) If a company acts as a cash cow, it will pay out a $10 dividend every year starting one year from today. These payments will continue forever. The appropriate effective annual discount rate for the stock is 5%. This company can retain its entire earnings 2 years from today (which means that a dividend will not be paid if the earnings are retained). If the earnings are retained, there is a 40% chance that the total dividend paid in 4 years will be $50 (with the other 60% probability of the usual $10 dividend). The dividend that will be paid in 4 years will be announced in 2.5 years. No other changes in dividends occur if the earnings 2 years from now are retained. There is also a European call option available to purchase, with a $205 exercise price and an expiration date 3 years from today (The option can only be exercised after the dividend on the same date is paid). The appropriate effective annual discount rate for the option is 25%. If the company decides to retain its earnings 2 years from today, what is the present value of the option?

Problem 3 As cash cow, FV 3 = 10 .05 =200 If investment is made, 60% of chance of stock FV 3 = 10 .05 =200 <205 40% chance of stock FV 3 = 10 .05 + 40 1.05 =238.0952>205. So there is a 40% of chance that the option will be “in the money”. Expected value of option in year 3 FV 3 =.4∗ 238.0952−205 +.6∗0= 13.2381 Expected present value of option P𝑉 = 13.2381 1+25% 3 =6.77790

Problem 4 Answer each of the following in 60 words or less. (a) (3 points) Explain the key characteristics of the bubble theory. Previous market conditions stable Euphoria Bubble bursts after euphoria Little regard for long run performance Deviation from efficient market hypothesis.

Problem 4 (b) (3 points) Explain the key characteristics of the efficient market hypothesis (EMH). Since prices change immediately to reflect new information, any investor should get the normal rate of return. Firms cannot fool investors into thinking that the price of a stock is higher than what it should be, given the value of the firm.

Problem 5 (6 points) Jackie Bowman is interested in buying stock in the Psycke Shoe Company. She knows that stock in the company has a beta value of 3.5, and that the stock is expected to pay a $2 dividend every six months (per share), starting four months from today. The market rate of return is 14%, and the risk-free rate is 3%. What is the present value of a share of this stock?  

Problem 5 Answer: The stock’s annual discount rate: Six month rate = 1+41.5% −1=18.9538% P𝑉 = 2 18.9538% 1+18.9538% 1/3 =11.1805

Problem 6 (5 points) Suppose that a zero-coupon US government bond sold for $800 on January 3, 2016. When sold on this date, the yield to maturity (as an effective annual rate) was 3.41%. The maturity date for this bond will be January 3, 2036. If the yield to maturity for the same bond on January 3, 2018, was 3.29%, what did this bond sell for on this date? 

Problem 6 Answer: FV 30 =800∗ 1+3.41% 20 =1,564.37 FV 2 = 1,564.37 1+3.29% 18 =873.56

Problem 7 (6 points) Catriona is about to buy her first Irish farm. She will receive $400,000 today to buy the farm, and another $100,000 in 3 years to build a barn. She must make 30 equal annual payments of $N in order to completely pay off both payments made to her (starting in 1 year). Find N if the stated annual interest rate is 4.2%, compounded monthly.

Problem 7 Answer: Monthly rate = 4.2%/12 = .35% EAR = 1+.35% 12 −1=4.28% 488,180.88= 𝑁 4.28% ∗ 1− 1 1+4.28% 30 N = 29,199.95