Question

You purchased a coupon bond on January 2, 2020 with the following information:

Coupon rate: 6.00% Interest payment: annual Maturity: 5 years

Par Amount: $10,000 Yield to Maturity: 6.20%

33.1 – What price did you pay for this bond? Show all calculations.

33.2 – If you sold the bond exactly two years later at a price of $101, what is your annualized rate of return for the two years, assuming you did not reinvest any coupon payments?

Answer 1

33.1

To find the present value of the bond, we discount all the future cash inflows to present day using the YTM as discount rate.

Cash Flows = Coupon for 5 years and Par value at end of 5th Year.

Year 1 - 600
Year 2 - 600
Year 3 - 600
Year 4 - 600
Year 5 - 600 + 10,000 = 10600

All the cash flows will be discounted and added to get the present value.

PV = [600/(1.062)^1] + [600/(1.062)^2] + [600/(1.062)^3] + [600/(1.062)^4] + [10600/(1.062)^5]

= 9,916.21

33.2

Annualized Rate of return = (Selling Price / [Cost of Investment - PV (Cash Inflows)]^(1 / Time) - 1) * 100

Cost of investment = 99.16

Present value of these cash inflows = 6/(1.062) + 6(1.062^2)

= 10.97

Annualized Rate of return = [101 / (99.16-10.97)]^ 0.5

= 7.01%