As per HOMEWORKLIB RULES, we are required to answer the first one question if multiple independent questions are given. So we have answered the first one. Hope you understand as we are to comply guidelines.
Determination of Issue Price of Bonds on January 1 of this year :- | ||||
Face Value of Bonds | = | $504,500 | ||
Life of Bond (in years) | = | 10 | ||
Maturity amount of Bond | $504,500 | |||
Coupon rate | = | 6% per year payable semi annually i.e. 3% per semi annual | ||
Semi annual Coupon Amount | = | $504,500 | × | 3% |
= | $15,135 | This will be paid 20 times | ||
n | = | 10 years i.e. 10 * 2 = 20 semi annuals | ||
Case A : | Market Interest Rate (annual) : 4 percent | |||
Market rate on similar bonds (r) | = | 4% | ||
= | 2% semi annual | |||
PVAF(r, n) | = | Present Value Annuity factor at r% for n periods | ||
Present Value of an Annuity of $1 at 2% for 20 periods | = | 16.3514333 | ||
PVIF(r, n) | = | Present Value interest factor at r% for n periods | ||
Present Value of $1 at 2% at n= 20 periods | = | 0.6729713 | ||
Price of Bond | = | Coupon Amount * PVAF(r,n) | + | Redemption Amount * PVIF(r,n) |
= | $15135* 16.3514333 | + | $504500* 0.6729713 | |
= | $247,479 | + | $339,514 | |
= | $586,993 | |||
Case B : | Market Interest Rate (annual) : 6 percent | |||
Market rate on similar bonds (r) | = | 6% | ||
= | 3% semi annual | |||
PVAF(r, n) | = | Present Value Annuity factor at r% for n periods | ||
Present Value of an Annuity of $1 at 3% for 20 periods | = | 14.8774749 | ||
PVIF(r, n) | = | Present Value interest factor at r% for n periods | ||
Present Value of $1 at 3% at n= 20 periods | = | 0.5536758 | ||
Price of Bond | = | Coupon Amount * PVAF(r,n) | + | Redemption Amount * PVIF(r,n) |
= | $15135* 14.8774749 | + | $504500* 0.5536758 | |
= | $225,171 | + | $279,329 | |
= | $504,500 | |||
Case C : | Market Interest Rate (annual) : 8.5 percent | |||
Market rate on similar bonds (r) | = | 8.5% | ||
= | 4.25% semi annual | |||
PVAF(r, n) | = | Present Value Annuity factor at r% for n periods | ||
Present Value of an Annuity of $1 at 4.25% for 20 periods | = | 13.2943658 | ||
PVIF(r, n) | = | Present Value interest factor at r% for n periods | ||
Present Value of $1 at 4.25% at n= 20 periods | = | 0.4349895 | ||
Price of Bond | = | Coupon Amount * PVAF(r,n) | + | Redemption Amount * PVIF(r,n) |
= | $15135* 13.2943658 | + | $504500* 0.4349895 | |
= | $201,210 | + | $219,452 | |
= | $420,662 |
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