Question

Consider a bond that promises to make coupon payments of $100 one year from now and $100 two years from now, and to repay the principal of $1,000 three years from now. Suppose also that the market interest rate is 8 percent per year, and that no perceived risk is associated with the bond. 8.1 Compute the present value of this bond.

1. Suppose the bond is being offered for $995. Would you buy the bond at that price? What do you expect to happen to the bond price in the very near future?
2. Suppose the bond is instead being offered for $950. Would you buy the bond at that price? Do you expect the bond price to change in the near future?
3. If the price of the bond is equal to its computed present value from [1], what is the implied bond yield?

Answer 1

The present value of the bond with coupon payments is calculated using the formula for present value and discounted at the market interest rate of 8%. If offered at $995, the bond is overvalued; at $950, it's undervalued. The bond yield matches the discount rate when the bond's price equals the computed present value.

Step-by-step explanation:

To calculate the present value of the bond, we discount each payment at the market interest rate of 8%. The present value calculation is done using the formula PV = C / (1+r)^t, where C is the cash flow, r is the discount rate, and t is the time in years. Applying this to the bond payments, we have:

• Year 1: PV = $100 / (1 + 0.08)^1 = $92.59
• Year 2: PV = $100 / (1 + 0.08)^2 = $85.73
• Year 3 (Coupon + Principal): PV = ($100 + $1000) / (1 + 0.08)^3 = $794.16

The total present value of the bond is the sum of these, which is $92.59 + $85.73 + $794.16 = $972.48.

If the bond is offered for $995:

1. You might hesitate to buy the bond since its price is above the present value, anticipating that the price may drop closer to the present value in the near future.

If the bond is offered for $950:

1. This price is below the present value, and buying it could be a good investment, as its market value could potentially rise to match the present value.

When the bond's price equals its present value, the market yield equals the discount rate used in the present value calculation, implying that the bond yield would also be 8%.