
Ascertain the issue price if the bonds are priced to yield (a) 10% (b) 8% and (c) 12%.

Explanation of Solution
Bonds:
A bond (long term debt) is a written document and a signed promise to pay interest periodically as well as the principal amount borrowed at the time of maturity to the bond investor.
(a)
Calculate the issue price of the 10%, 5-year, $100,000 bonds if the market interest rate 10 % is payable semiannually.
Therefore, the issue price of the bonds is $100,000.
Working notes:
Calculate the present value for 5 periods and 10% interest compounded semiannually:
Note:
When present value is compounded semiannually, the number of years will be doubled and the rate of interest will decrease by half of the given interest rate.
(1)
Calculate the Present value of face value of bonds:
Particulars | Amount ($) |
Face value of bonds (a) | 100,000 |
PV factor at a semiannual market rate of 5% for 10 periods (b) (1) | 0.614 |
Present value of face value of the bonds | 61,400 |
(Table 1)
(2)
Calculate stated semiannual interest rate:
Calculate the interest payable:
Calculate the present value factor for semiannual market of 5% for 10 periods:
Calculate present value of interest payments:
Particulars | Amount ($) |
Interest payable amount (a) | $5,000 |
PV factor at a semiannual market rate of 5% for 10 periods (b) (5) | 7.722 |
Present value of interest payments | 38,600 |
(Table 2)
(6)
(b)
Calculate the issue price of the 10%, 5-year, $100,000 bonds if the market interest rate 8% is payable semiannually.
Therefore, the issue price of the bonds is $108,155.
Working notes:
Calculate the present value for 5 periods and 8% interest compounded semiannually:
Note:
When present value is compounded semiannually, the number of years will be doubled and the rate of interest will decrease by half of the given interest rate.
(7)
Calculate the Present value of face value of bonds:
Particulars | Amount ($) |
Face value of bonds (a) | 100,000 |
PV factor at a semiannual market rate of 4% for 10 periods (b) (7) | 0.676 |
Present value of face value of the bonds | 67,600 |
(Table 3)
(8)
Calculate the present value factor for semiannual market of 4% for 10 periods:
Calculate present value of interest payments:
Particulars | Amount ($) |
Interest payable amount (a) | $5,000 |
PV factor at a semiannual market rate of 4% for 10 periods (b) (9) | 8.111 |
Present value of interest payments | 40,555 |
(Table 4)
(10)
(c)
Calculate the issue price of the 10%, 5-year, $100,000 bonds if the market interest rate 12% is payable semiannually.
Therefore, the issue price of the bonds is $92,600.
Working notes:
Calculate the present value for 5 periods and 12% interest compounded semiannually:
Note:
When present value is compounded semiannually, the number of years will be doubled and the rate of interest will decrease by half of the given interest rate.
(11)
Calculate the Present value of face value of bonds:
Particulars | Amount ($) |
Face value of bonds (a) | 100,000 |
PV factor at a semiannual market rate of 6% for 10 periods (b) (11) | 0.558 |
Present value of face value of the bonds | 55,800 |
(Table 5)
(12)
Calculate the present value factor for semiannual market of 6% for 10 periods:
Calculate present value of interest payments:
Particulars | Amount ($) |
Interest payable amount (a) | $5,000 |
PV factor at a semiannual market rate of 6% for 10 periods (b) (13) | 7.360 |
Present value of interest payments | 36,800 |
(Table 6)
(14)
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