Question

Cecilia wants to purchase a bond that pays no coupon for the first 4 years. The bond will then make annual payments of $200 each year for 5 years, after which the bond will then make $300 annual payments in perpetuity. How much is this bond worth if the yield to maturity is 6%?

Answer 1

Present value of an amount is computed as -

PV = Amount / (1 + r)ⁿ

where, r is the discount rate and n being the year for which it is calculated.

In our case, the yield to maturity (YTM) is the discount rate.

So, we need to compute the present value of coupons in years 5 to 9 and present value of perpetual cash flows.

Value of perpetual cash flows at the end of year 9 = $300 / 6% = $5000

Bond Value = [ $200 / (1 + 0.06)⁵ ] + [ $200 / (1 + 0.06)⁶ ] + [ $200 / (1 + 0.06)⁷ ] + [ $200 / (1 + 0.06)⁸ ] + [ $200 / (1 + 0.06)⁹ ] + [ $5000 / (1 + 0.06)⁹ ]

or, Bond value = $3626.80965 or $3626.81