Question

The YTM on a bond is the interest rate you earn on your investment if interest rates don’t change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY).

a.	Suppose that today you buy a bond with an annual coupon rate of 8 percent for $1,100. The bond has 15 years to maturity. What rate of return do you expect to earn on your investment? Assume a par value of $1,000. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b-1.	Two years from now, the YTM on your bond has declined by 1 percent, and you decide to sell. What price will your bond sell for? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b-2.	What is the HPY on your investment? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

a.	Expected Rate of Return		%
b-1.	Bond Price
b-2.	HPY		%

Answer 1

Part A:
Face Value of the Bond = $1000
Annual Coupon Rate = 8%
Current Purchase Price = $1100
Time to Maturity = 15 years

Coupon Amount = Face Value * Annual Coupon Rate
= 1000*8%
= 80.

Cash Outflow at t = 0 --> -1100 for purchase of bond
Cash Inflow at t = 1 to t = 15 from coupon --> +80
Additional Cash inflow at t=15 from redemption of bond --> +1000

More formally,
CF₀ = -1100
CF₁ to CF₁₄ = +80
CF₁₅ = 80+1000 = 1080

Assume Rate of Return = r, then setting up the Net Present Value of CasfhFlows should be zero -

0 = CF₀ + CF₁/(1+r)^1 + CF₂/(1+r)^2 + CF₃/(1+r)^3 + ........... + CF₁₅/(1+r)^15
Solving above equation for r will give is the required rate of return.

This equation can be solved easily in Excel as given below. Formulas in excel look like below -

Values in excel look like below -


Now, Simply apply "IRR" Formula of excel on Total Cashflow column to get rate of return on investment -

Hence, value of r = 6.91%
Answer - Expected Return = 6.91%

Part B:
Current Yield = 6.91%
2 years later, yield y = 6.91% - 1.00% = 5.91%

Consider the following cashflows for this scenario -
CF₃ to CF₁₄ = 80 from coupon payment
CF₁₅ = 80 from coupon payment + 1000 from redemption of bond = 180

As we are calculating price of the bond at the end of 2 years, equation will look like below -

Price of Bond = CF3/(1+r) + CF4/(1+r)^2 + CF5/(1+r)^3 + ..................... + CF15/(1+r)^13

Using this in excel, formulas will look like below -

Values in excel will look like below -

Answer - Bond Price after 2 years = $1186.00

Part C:
For holding period following cashflows occur for the investor -
CF0 = -1100 towards purchase of the bond
CF1 = +80 from the coupon payment
CF2 = +80 from coupon payment and +1186 by sale of the bond.

If HPY = r , following equation can be written -

0 = CF₀ + CF₁/(1+r)^1 + CF₂/(1+r)^2
Solve above equation for value of r to get HPY.

This can be done easily in excel, formulas will look like below -

Values in excel will look like below -

Answer : HPY = 10.98%