1. An investment offers a total return of 12 percent over the coming year. Bill
ID: 2773372 • Letter: 1
Question
1. An investment offers a total return of 12 percent over the coming year. Bill Bernanke thinks the total real return on this investment will be only 7.3 percent.
What does Bill believe the inflation rate will be over the next year?
2. Say you own an asset that had a total return last year of 15 percent. Assume the inflation rate last year was 4.3 percent.
What was your real return?
3. PK Software has 8.1 percent coupon bonds on the market with 24 years to maturity. The bonds make semiannual payments and currently sell for 109.5 percent of par.
What is the current yield on PK's bonds?
What is the YTM?
What is the effective annual yield?
4. BDJ Co. wants to issue new 19-year bonds for some much-needed expansion projects. The company currently has 8.8 percent coupon bonds on the market that sell for $1,128, make semiannual payments, and mature in 19 years.
What coupon rate should the company set on its new bonds if it wants them to sell at par?
Required:What does Bill believe the inflation rate will be over the next year?
2. Say you own an asset that had a total return last year of 15 percent. Assume the inflation rate last year was 4.3 percent.
Required:What was your real return?
3. PK Software has 8.1 percent coupon bonds on the market with 24 years to maturity. The bonds make semiannual payments and currently sell for 109.5 percent of par.
Requirement 1:What is the current yield on PK's bonds?
Requirement 2:What is the YTM?
Requirement 3:What is the effective annual yield?
4. BDJ Co. wants to issue new 19-year bonds for some much-needed expansion projects. The company currently has 8.8 percent coupon bonds on the market that sell for $1,128, make semiannual payments, and mature in 19 years.
Required:What coupon rate should the company set on its new bonds if it wants them to sell at par?
Explanation / Answer
Answer 1
( 1 + nominal rate) = ( 1 + real rate) * (1 + inflation)
Or ( 1 + 12% ) = ( 1 + 7.3%) *( 1 + inflation)
Or ( 1 + inflation) = 1.0438
Or Inflation = 0.0438 = 4.38%
Answer 2
Using the formula above , now we will calculate real return
( 1 +15% ) = ( 1 + real rate) * ( 1 + 4.3%)
Or ( 1 + real rate) = ( 1 +15% ) / ( 1 + 4.3%)
Or ( 1 + real rate) = 1.10259
Or Real Rate = 10.26%
Answer 3
Bond Face Value = 100
Bond Price Today = 109.5% of 100 = 109.50Coupon Rate = 8.1% , semiannual coupon payments = 8.1% of 100 / 2 = 4.05
Time to maturity = 24 years ; = 24 *2 = 48 compounding periods
Current yield on a bond is calculated as the annual cash inflows from the bond divided by the current market price
Hence Current yield = Coupon Received / Market Price = 8.1 / 109.50 * 100 = 7.397%
Yield to maturity on bond can be calculated as the present value of all the coupon payments and the bond face value received at the end of term of bond.
By using a financial calculator, and inputting the above values, we can calculate the discounting rate which would be the YTM (Note: we can also use the PVIFA table)
Present Value = 109.5 ; Future Value = 100 ; N = 48 ; Coupon = 4.05
Yield = 3.63% semi annual
Hence annual yield = 3.63 * 2 = 7.26%
Effective Annual Yield = (1 + semi annual YTM)^ 2 – 1
Effective Annual Yield = ( 1 + 3.63%) ^ 2 – 1 = 1.07392 – 1 = 7.39%
Answer 4
For a bond that sells at par, its coupon rate must equal the market rate( the rate at which the cash inflows and outflows are discounted)
If we calculate the YTM on the comparable bond, we will know the coupon rate for new bond as coupon rate = YTM in case of bond selling at par.
So For YTM, compounding period = 19 *2 = 38 ; Face value = 1000 ; Market Value = 1128 ;
Semi Annual Coupon = 8.8% of 1000 / 2 = 44
By inputting the above in excel ( use rate function) we will get the YTM of bond as 3.76%
This is however the semi annual yield ; so annual yield = 3.76 * 2 = 7.52%
So in order for the new bonds to be sold at par, coupon rate must be set to market rate (YTM) = 7.52%
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