You bought one of Bergen Manufacturing Co.’s 7.8 percent coupon bonds one year a

Question

You bought one of Bergen Manufacturing Co.’s 7.8 percent coupon bonds one year ago for $1,061. 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 4.4 percent over the past year, what would be your total real return on the investment? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)

You bought one of Bergen Manufacturing Co.’s 7.8 percent coupon bonds one year ago for $1,061. 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.

Explanation / Answer

To determine the real rate of return we, need to calculate the nominal rate of return. To calculate the nominal rate of return we need to determine the price after 1 year.

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Step 1: Calculate Bond's Price Today

Bond price can be calculated with the use of EXCEL/Financial Calculator. The formula/function used for the same is: PV(Rate,Nper,PMT,FV) where PV is the price, Nper is the period, PMT is the annual interest payment and FV is the face value.

If we pick values from the question, Rate = 4.5%, Nper = 12 (only the remaining period), PMT = 1,000*7.8% = $78 and FV = $1,000

Substiuting these values in the EXCEL/Financial Calculator function, we get:

Price Today = PV(4.5%,12,78,1000) = $1,300.91

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Step 2: Calculate Nominal Rate of Return

The formula for nominal rate of return is: (Capital Gain + Coupon Payment)/Original Price*100

Capital gain results from increase in the price of bond over the period.

Capital Gain = Price Today - Purchase Price = $1,300.91 - $1,061 = $231.91

Using the values calculated above.

Nominal Rate of Return = ($231.91 + $78)/1061*100 = 29.21%

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Step 3: Calculate Real Rate of Return

The formula for real rate of return = (1+Nominal Rate of Return)/(1+Inflation Rate) - 1

Using Values calculated above and provided in the question,

Real Rate of Return = (1+29.21%)/(1+4.4%) - 1 = 23.76%

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