Question

Question 1 (5 marks) Georgina and Harvey are expecting their first child. They would like to establish a savings plan to help cover the child's university expenses. Between them they figure they can put aside $10 per week. They will deposit the money in a savings account earning 2.6% APR compounded weekly The first deposit will be made when the baby is 1 week old, and the final de,CLOSE will be on the child's 18th birthday. How much money will be in the account after the last deposit is made? Question 2 (10 marks) Lizzie is investing in a BigTop Ltd corporate bond. The bond matures in exactly 7 years, has a face value of $1000 and a coupon rate of 7.5% pa. with semi-annual coupons. The current yield to maturity on these bonds is 6.9% pa. (all interest rates are given as annual percentage rates and compounding is semi-annual) Without any computations, will the bond sell for more or less than the $1000 face value? (1 mark) a. CLOS b. What is the current price of BigTop Ltd bonds? (4 marks) Explain why bond prices and interest rates are negatively related. Explain why this relationship is more or less prominent for higher coupon bonds. (5 marks) c. Question 3 (10 marks) Orchard Lakes Ltd shares are currently selling for $44 and are expected to pay a dividend of $4.75 in one year. Investors require a return of 15% on Orchard Lakes shares. a. What perpetual growth rate has the market priced in to Orchard Lakes shares? (4 marks) CI b. Based on the growth rate computed in (a), what do you expect Orchard Lakes shares to sell for in 4 years? (2 marks) Discuss the restrictions on reasonable values for the perpetual growth rate. Be sure to mention both the mathematical restrictions and the economic restrictions. (4 marks) c.

Answer 1

1). Number of periods N = 18*52 = 936

Interest rate = 2.5%/52 = 0.050%

PMT (weekly deposit) = 10

Solve for FV. FV = 11,932.21 (amount after 18 years)

2a). Bond will be selling for more than par value since current yield is less than coupon rate.

2b). Current yield = annual coupon/current price

current price = annual coupon/current yield

= (7.5%*1000)/6.9% = 1,086.96

2c). Bond price is calculated as the sum of the present value of all future cash flows. As interest rates increase, the discounted cash flows decrease and vice-versa. Thus, bond prices and interest rates are inversely proportional. For a higher coupon bond, the effect is less prominent as compared to lower coupon bonds.

3a). Using DDM model,

required return = expected dividend/share price + growth rate

15% = (4.75/44) + g

g = 4.20%

3b). Dividend after 5 years will be 4.75*(1+g)^4 = 4.75*(1+4.20%)^4 = 5.60

Share price after 4 years = expected dividend/(required return - growth rate)

= 5.60/(15%-4.20%) = 51.88

3c). Perpetual growth rate has to be lower than the required return otherwise the formula for perpetual value will not work. If perpetual growth rate is greater than required return then it is considered abnormal growth and cash flows for each year has to be calculated separately till the growth rate settles down to a lower, stable number. Similarly, the perpetual growth rate cannot exceed the growth rate of the economy (since it will imply that the company will always outperform the economy which is not possible) and it cannot be negative.