Question

You bought one of Bergen Manufacturing Co.’s 5.4 percent coupon bonds one year ago for $1,053. These bonds make annual payments and mature twelve years from now. Suppose you decide to sell your bonds today when the required return on the bonds is 4.5 percent.

  

If the inflation rate was 3.8 percent over the past year, what would be your total real return on the investment? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

  

Total real return

%

Answer 1

Market Price of the Bond

The Market Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the face Value

Face Value of the bond = $1,000

Annual Coupon Amount = $54 [$1000 x 5.40%]

Annual Yield to Maturity = 4.50%

Maturity Period = 12 Years

Therefore, the Market Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $54[PVIFA 4.50%, 12 Years] + $1,000[PVIF 4.50%, 12 Years]

= [$54 x 9.11858] + [$1,000 x 0.58966]

= $492.41 + $589.66

= $1,082.07

Nominal Rate of Return on the Bond

Nominal Rate of Return on the Bond = [{Annual Coupon Amount + (Change in Bond Price)} / Current Price] x 100

= [{$54 + ($1,082.07 - $1,053} / $1,053] x 100

= [($54 + $29.07) / $1,053] x 100

= [$83.07 / $1,053] x 100

= 7.89%

Real Rate of Return on Investment

Real Rate of Return on Investment = [(1+Nominal Rate of Return)/(1+Inflation Rate)] - 1

= [(1 + 0.0789) / (1 + 0.0380)] – 1

= [1.0789 / 1.0380] – 1

= 1.039389456 – 1

= 0.039389456 or

= 3.94%

“Hence, the Total Real Return will be 3.94%”

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)ⁿ} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.

-The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.