The face value is $ 92 comma 000$92,000, the stated rate is 1010%, and the term

Question

The face value is $ 92 comma 000$92,000, the stated rate is 1010%, and the term of the bond is eight years. The bond pays interest semiannually. At the time of issue, the market rate is 88%. What is the present value of the bond at the market rate? Present value of $1: 4% 5% 6% 7% 8% 15 0.555 0.481 0.417 0.362 0.315 16 0.534 0.458 0.394 0.339 0.292 17 0.513 0.436 0.371 0.317 0.270 18 0.494 0.416 0.350 0.296 0.250 19 0.475 0.396 0.331 0.277 0.232 Present value of annuity of $1: 4% 5% 6% 7% 8% 15 11.118 10.380 9.712 9.108 8.559 16 11.652 10.838 10.106 9.447 8.851 17 12.166 11.274 10.477 9.763 9.122 18 12.659 11.690 10.828 10.059 9.372 19 13.134 12.085 11.158 10.336 9.604 A. $ 102 comma 727$102,727

Explanation / Answer

Face value of Bonds

$92,000

Standard rate

10%

Standard rate semi annual

5%

Term

8 years

Interest payable

Semi annually

Market rate

8%

Market rate semi annual

4%

Calculation of Present value of Bond

Semi-annual interest for 16 periods @ 5% per half year
($92,000*5%)

$4,600

Annuity factor for 16 periods @4%

11.6523

(A)

P.v of future interest cash flows

$53,601

redemption value

$92,000

P.v Factor @ 4% at 16 periods

0.53391

(B)

P.v of Redemption value of Bonds

$49,120

(C)

Total P.V of cashflows

$102,720

Present value of Bond = $102,720

Face value of Bonds

$92,000

Standard rate

10%

Standard rate semi annual

5%

Term

8 years

Interest payable

Semi annually

Market rate

8%

Market rate semi annual

4%

Calculation of Present value of Bond

Semi-annual interest for 16 periods @ 5% per half year
($92,000*5%)

$4,600

Annuity factor for 16 periods @4%

11.6523

(A)

P.v of future interest cash flows

$53,601

redemption value

$92,000

P.v Factor @ 4% at 16 periods

0.53391

(B)

P.v of Redemption value of Bonds

$49,120

(C)

Total P.V of cashflows

$102,720

Present value of Bond = $102,720

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