Consider a coupon bond that has a $1,000 par value and a coupon rate of 10%…

Question:

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  1. Consider a coupon bond that has a $1,000 par value and a coupon rate of 10%. The bond is currently selling for $1,235 and has 8 years to maturity. What is the bond’s yield to maturity?
  2. You are willing to pay $14,412 now to purchase a consol bond which will pay you and your heirs $1,225 each year, starting at the end of this year. If your required rate of return does not change, how much would you be willing to pay if this were a 20-year, annual payment, ordinary annuity instead of perpetuity?
  3. Assume you just deposited $1,000 into a bank account. The current real interest rate is 2% and inflation is expected to be 6% over the next year. What nominal interest rate would you require from the bank over the next year? How much money will you have at the end of one year? If you are saving to buy a stereo that currently sells for $1,050, will you have enough to buy it?

Answer:

Coupon payment = 0.1 * 1000 = 100
Yield to maturity using a financial calculator = 6.19%
Keys to use in a financial calculator: PV -1235, PMT 100, N 8, FV 1000, CPT I/Y
5) Present value of perpetuity = Annual cash flow / Required rate
14,412 = 1,225 / Required rate
Required rate = 0.0849 or 8.5%
Present value of annuity = Annuity * [ 1 – 1 / ( 1 + r)n] / r
Present value of annuity = 1,225 * [ 1 – 1 / ( 1 + 0.085)20] / 0.085
Present value of annuity = 1,225 * 9.463
Present value of annuity = $11,592.18
6) Nominal interest rate = 6% + 2% = 8%
Money at the end of the year = 1000 * 1.08 = $1,080
The price of stereo will increase at the rate of inflation
Price of steroeo = 1050 * 1.06 = $1,113
You will NOT have enough to buy it

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