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Economics - Money & Banking

Q1. A bond you are evaluating has $1,000 face value, 8% coupon rate (paid annually) and 4 years remaining to maturity. Calculate its present value if the market rate of interest is:
(a) 10% : $ _________
(b) 8% : $ _________
(c) 6% : $_________
(d) What do your answers to (a) through (c) say about the relationship between bond prices and interest rates?

Q2. Assuming a market rate of interest of 8%, 10% and 12%, calculate the present value of the following bonds, all of which have a coupon rate of 10% (paid annually) and face value of $1,000.
(a) Bond A has 10 years remaining to maturity: $_________
(b) Bond B has 5 years remaining to maturity: $_________
(c) Bond C has 1 year remaining to maturity: $_________
(d) What do your answers to parts (a) through (c) say about the relationship between term to maturity and bond price volatility?

Q3. You purchased a $1,000 face value bond with a 5% coupon rate and 4 years remaining to maturity when the market rate of interest was 6% and sold two years later when market rate was 8%. Calculate your holding period return.

Q4 Suppose that in exchange for allowing a road pass through his land, Farmer George has been paid $2,500 per year by the township he lives in. He had been promised that he and future owners of his land would receive this payment in perpetuity. Now, however, the township has offered and he has accepted a one time payment of $30,000, in exchange of his giving up the right to receive the annual payment. What implicit interest rate Farmer George and the township used in arriving at this settlement?
_____%

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Q1. A bond you are evaluating has $1,000 face value, 8% coupon rate (paid annually) and 4 years remaining to maturity. Calculate its present value if the market rate of interest is:

(a) 10% : $ _________
Coupon amount=C=1000*8%=$80
Number of coupon payments left=n=4
Maturity amount=Face Value=M=$1000
Market interest Rate=i=10%

Fair Value of bond at the time of purchase= C/i*(1-1/(1+i)^n)+M/(1+i)^n

Fair Value of bond at the time of purchase
= 80/10%*(1-1/(1+10%)^4)+1000/(1+10%)^4
=$936.60

(b) 8% : $ _________
Coupon amount=C=1000*8%=$80
Number of coupon payments left=n=4
Maturity amount=Face Value=M=$1000
Market interest Rate=i=8%

Fair Value of bond at the time of purchase= C/i*(1-1/(1+i)^n)+M/(1+i)^n

Fair Value of bond at the time of purchase
= 80/8%*(1-1/(1+8%)^4)+1000/(1+8%)^4
=$1000

(c) 6% : $_________
Coupon amount=C=1000*8%=$80
Number of coupon payments left=n=4
Maturity amount=Face Value=M=$1000
Market interest Rate=i=6%

Fair Value of bond at the time of purchase= C/i*(1-1/(1+i)^n)+M/(1+i)^n

Fair Value of bond at the time of purchase
= 80/6%*(1-1/(1+6%)^4)+1000/(1+6%)^4
=$1069.30

(d) What do your answers to (a) through (c) say about the relationship between bond prices and interest rates?
We find that if market interest rate is less than coupon rate, bond is selling at a premium.
If market interest rate is equal to coupon rate, bond is selling at par.
If market interest rate is greater than coupon rate, bond is selling at a discount.

Q2. Assuming a market rate of interest of 8%, 10% and 12%, calculate the present value of the following bonds, all of which have a coupon rate of 10% (paid annually) and face value of $1,000.
(a) Bond A has 10 years remaining to maturity: $_________
Market Interest Rate=8%
Coupon ...

Solution Summary

There are 4 questions. Solutions to first two problems describe the methodology to estimate the price of coupon bonds. Solution to third problem depicts the methodology to calculate holding period return in the given case. Solution to fourth problem calculates the implicit rate of interest.

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