Download Exam Preparation Assignment 4 Version 1: ANSWER KEY

Exam Preparation Assignment 4 Version 1:
ANSWER KEY
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1. Suppose you will receive $500,000 each year for the next three years beginning in 1
year. Calculate the present value of this sequence of payments when the interest rate is:
With a constant interest rate as in this question, the discount factors for the next 3 years are
1/(1+i), 1/(1+i)2, 1/(1+i)3 respectively. Therefore $Vt = 500,000*(1/(1+i)) + 500,000*(1/(1+i)2) +
500,000*(1/(1+i)3) and you simply need to plug in the interest rate!
a. 0%
When i =0, $Vt is just the sum of the payments which is $1,500,000.
b. 5%
When i = 5%, $Vt = $1,361,624.01
c.
10%
When i =10%, $Vt = $1,243,425.99
d. What happens to the present value of this sequence of payments as the interest
rate rises? Explain.
The higher the interest rate, the lower the resulting present value. This is because as i increases
the discount factor increases and so the weights of future payments become smaller.
2. A “consol” promises to pay $500 each year, forever, starting next year. If the nominal
interest rate is 10%, what is the present discounted value of this consol?
Recall that the present value of a consol is $Vt = $Z/i. Therefore:
$Vt = $500/0.10 = $5000.00
Exam Preparation Assignment #4
ANSWER KEY
ECON 2470
1
3. Determine the yield to maturity of each of the following bonds:
a. A discount bond with a face value of $1,000, a maturity of three years, and a
price of $800.
1+i =($F/$P)1/n
i =(1000/800)1/3-1 = 7.7%
b. A discount bond with a face value of $1,000, a maturity of four years, and a price
of $800.
5.7%
c.
A discount bond with a face value of $1,000, a maturity of four years, and a price
of $850.
4.1%
4. Suppose a coupon bond promises $100 coupon payments and has a face value of
$1000. The current price of the bond is $850.
a. What is the coupon rate for this bond?
Coupon rate = 10%
Recall coupon rate is ratio of coupon payments to the face value =$100/$1000
b. What is the current yield on his bond?
Current yield = 11.76%
Recall, current yield is ratio of coupon payments to the current price of the bond =$100/$850.
5. Suppose the interest rate this year is 5% and financial markets expect the interest rate to
increase by 0.5% (50 basis points) each year for the following three years. Determine the
yield to maturity on a
a. One-year bond = 5%.
b. Two-year bond = 5.25%
c.
Three-year bond = 5.5%
6. Suppose the Bank of Canada implements a contractionary monetary policy that is at least
partially unexpected. Explain what effect this will have on stock prices.
This contractionary monetary policy will cause the interest rate to rise and output to fall. The
higher interest rate will reduce the present value of future dividends. The reduction in output will
cause a reduction in expected dividends because profits are now expected to be lower. Both of
these effects will cause stock prices to fall.
Exam Preparation Assignment #4
ANSWER KEY
ECON 2470
2
7. A share of stock will pay a dividend of $10 in one year, and will be sold for an expected
price of $100 at that time (ex-dividend price). If the current one-year interest rate is 5%,
then what is the current price of the stock?
$Qt = (10/1.05) + (100/1.05)= $104.76
Exam Preparation Assignment #4
ANSWER KEY
ECON 2470
3