$1,000
Step 1: Calculate the risk-free rate of the zero-coupon bond.
PV = FV ÷ (1+Risk-free rate)^Number of years
$924.56 = $1,000 ÷ (1+Risk-free rate)^2
(1+Risk-free rate)^2 = $1,000 ÷ $924.56
(1+Risk-free rate)^2 = 1.0815955
Risk-free rate = √1.0815955 - 1
Risk free rate = 0.040
= 4.00%
Step 2: Calculate the yield of the BB-corporate bond-
Yield = Risk-free rate + Credit spread
= 4.00% + 5.00%
= 9.00%
Step 3: Calculate the current price of the BB-corporate bond by using the following formula-
PV = [{Coupon × {1-(1+Yield)^-Number of years} ÷ Yield}+{Face value ÷ (1+Yield)^Number of years}]
= [{($1,000×9.00%)×{1-(1+9.00%)^-2 }÷ 9.00%}+{$1,000 ÷ (1+9.00%)^2}]
= $158.32 + $841.68
= $1,000
Since the coupon rate (CR) of the corporate bond has not been mentioned, it is assumed that the yield and CR are the same. When YTM and CR are equal, then the PV (present value) of the bond will always equal its face value.
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Consider the following bond: Face value = 1000; coupon rate = 8%; maturity = 5 years; ytm = 7% A) What is the value of the bond today and in 2 years? b) what are the current yield and capital gains yield for this bond this year and in two years? c) Assuming interest rates remain the same over this bond's lifetime, what is going to happen to the value of this bond as time goes by?
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Video Transcript
So here first, the face value is equal to 1000. Maturity is 5 years. The y t m is equal to 7. Coupon is equal to 8 percent multiplied by 1000. That is 80 point now. Price of bond today is equal to p v of coupons, plus p v of per per value, that is 80 multiplied by 1, minus 1 plus 7 percent to the power minus 5 upon 7 percent plus 1000 upon 1 plus 7 percent to the power 5. That is equal to 11041.02. The price of bond in 2 years is equal to 80 multiplied by 1, minus 1 plus 7 percent 7 percent to the power minus 3 upon 7 percent plus 1000 upon 1 plus 7 percent to the power 3, which is equal to 1026.2 4 point. Similarly, price of bond in 2 years or 1 year is equal to 1033.87. Second, the current yield is equal to coupon upon price that is 80 upon 1041.02, that is equal to 7.68 percent and the capital gain yield is equal to 1033.87 minus 1041.02 upon 1041.02. That is equal to minus .68 percent. The current yield in 2 years is 80 upon 1026.24, that is equal to 7.80 percent and the capital gain yield. Isy t m minus the current yield, that is 7 percent minus 7.80 percent, which is equal to minus 0.80 percent and third, as lifetime increases value of bond decreases.
Consider the following $1,000 par value zero-coupon bonds:
| Bond | Years to Maturity | YTM(%) |
| A | 1 | 5.9% |
| B | 2 | 6.9% |
| C | 3 | 7.4% |
| D | 4 | 7.9% |
According the the expectations hypothesis, what is the market's expectation of the yield curve one year from now? Specifically, what are the expected values of next year's yields on bonds with maturities of (a) one year? (b) two years? (c) three years (write answers as a percentage, rounded to 2 decimal places)?
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