Question

You own 30-year Treasury Bonds that you bought exactly 6 years ago. At the time (you bought the TBonds when they were issued), the 30-year T-Bond yield was 3.75% APR (compounded semiannually). That yield was also the coupon rate used to compute the semi-annual coupon payments (the T-Bonds were issued exactly at par). The T-Bonds have a total face value of $50,000. You just received an interest payment, and the bonds will mature in exactly 24 years. You check today’s yield curve for Treasuries, and the yield for such long-maturity T-Bonds is currently 1.40% (APR, compounded semi-annually).

a. What is the current market value of your T-Bonds?

b. By what percentage has the value of your T-Bonds increased or decreased since you bought them?

Answer 1

No of periods = 24 years * 2 = 48 semi-annual periods

Coupon per period = (Coupon rate / No of coupon payments per year) * Face value

Coupon per period = (3.75% / 2) * $50000

Coupon per period = $937.5

Bond Price = Coupon / (1 + YTM / Compounding frequency )^period + Face value / (1 + YTM / Compounding frequency )^period

T-Bond Price = $937.5 / (1 + 1.4% / 2)¹ + $937.5 / (1 + 1.4% / 2)² + ...+ $937.5 / (1 + 1.4% / 2)⁴⁸ + $50000 / (1 + 1.4% / 2 )⁴⁸

Using PVIFA = (1 - (1 + Interest rate)^{- no of periods} / interest rate to value coupons

T-Bond Price = $937.5 * (1 - (1 + 1.4% / 2)^-48) / (1.4% / 2) + $50,000 / (1 + 1.4% / 2 )⁴⁸

T-Bond Price = $38108.02 + $35,773.00

T-Bond Price = $73,881.03

At issuance the Bond was issued at yield = 3.75% & coupon rate = 3.75% which implies that the bond was issued at Par i.e. $50,000

Percentage increase in value of T-Bond = (Current T-Bond Price - T-Bond Price at issuance) / T-Bond Price at issuance

Percentage increase in value of T-Bond = ($73,881.03 - $50,000) / $50,000

Percentage increase in value of T-Bond = 47.76%

Annual percentage increase in value of T-Bond = (Percentage increase in value of T-Bond)^{(1 / no of years)}

Annual percentage increase in value of T-Bond = (47.76%)^{(1 / 6)}

Annual percentage increase in value of T-Bond = 8.84%