1) Even though most corporate bonds in the United States make coupon payments se
ID: 2776961 • Letter: 1
Question
1) Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of €1,000, 20 years to maturity, and a coupon rate of 7.4 percent paid annually.
If the yield to maturity is 8.5 percent, what is the current price of the bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
2) Cannonier, Inc., has identified an investment project with the following cash flows.
Year
Cash Flow
1
$
920
2
1,150
3
1,370
4
2,110
If the discount rate is 9 percent, what is the future value of these cash flows in Year 4? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
What is the future value at a discount rate of 12 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
What is the future value at a discount rate of 23 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
3) Find the EAR in each of the following cases (Use 365 days a year. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.):
Stated Rate (APR)
Number of Times Compounded
Effective Rate (EAR)
9.6
%
Quarterly
%
18.6
Monthly
14.6
Daily
11.6
Infinite
Year
Cash Flow
1
$
920
2
1,150
3
1,370
4
2,110
Explanation / Answer
1) Yield to Maturity = [(Face Value/Bond Price)1/Time period ] - 1
8.5% = [(€ 1000 / Bond Price)1/20 ] - 1
0.085 = [(1000 / Bond Price)0.05 ] - 1
0.085 + 1 = (1000/Bond Price)0.05
1.085 = 10000.05 / Bond Price0.05
Bond Price0.05 = 1.41 / 1.085
Bond Price = 0.051.30 = €190.05
2) Future Value (FV) = C0 * (1 + r)n where C0 = Cash flow at period 0, r = rate of return, n = no. of periods
i) r = 9%
FV = $920 * (1 + 9%)1 + $1150 * (1 + 9%)2 + $1370 * (1 + 9%)3 + $2110 * (1 + 9%)4
= 920 (1.09)1 + 1150 (1.09)2 + 1370 (1.09)3 + 2110 (1.09)4
= 1002.8 + 1366.32 + 1774.19 + 2978.44 = $7121.75
ii) r = 12%
FV = $920 * (1 + 12%)1 + $1150 * (1 + 12%)2 + $1370 * (1 + 12%)3 + $2110 * (1 + 12%)4
= 920 (1.12)1 + 1150 (1.12)2 + 1370 (1.12)3 + 2110 (1.12)4
= 1030.4 + 1442.56 + 1924.75 + 3320.13 = $7717.84
iii) r = 23%
FV = $920 * (1 + 23%)1 + $1150 * (1 + 23%)2 + $1370 * (1 + 23%)3 + $2110 * (1 + 23%)4
= 920 (1.23)1 + 1150 (1.23)2 + 1370 (1.23)3 + 2110 (1.23)4
= 1131.6 + 1739.84 + 2549.39 + 4829.51 = $10250.34
3) Effective Annual Rate (EAR) = (1 + i/n)n - 1 where i = stated annual interest rate, n = no. of compounding period
i) APR = 9.6%, Compounded Quarterly
EAR = (1 + 9.6% )4/365 - 1
4/365
= (1 + 0.096/0.01)0.01 - 1
= 10.60.01 - 1
= 1.02 - 1 = 0.02 or 2%
ii) APR = 18.6%, Compounded Monthly
EAR = (1 + 18.6% )12/365 - 1
12/365
= (1 + 0.186/0.03)0.03 - 1
= 7.20.03 - 1
= 1.06 - 1 = 0.06 or 6%
iii) APR = 14.6%, Compounded daily
EAR = (1 + 14.6% )365/365 - 1
365/365
= (1 + 0.146/1)1 - 1
= 1.146 - 1 = 0.146 or 14.6%
iv) APR = 11.6%, Compounded infinite times
EAR = (1 + 11.6% )/365 - 1
/365
This equation can not be solved since it has infinite numbers.
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