Financial Accounting for Undergraduates
Financial Accounting for Undergraduates
2nd Edition
ISBN: 9781618530400
Author: FERRIS
Publisher: Cambridge
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Chapter 10, Problem 16AE
To determine

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

Expert Solution & Answer
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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.

Issue price of bonds={Present value of principal (2)+Present value of interest payments (6)}=$61,400+$38,600=$100,000

Therefore, the issue price of the bonds is $100,000.

Working notes:

Calculate the present value for 5 periods and 10% interest compounded semiannually:

Present Value = 1(1+i)n=1(1+0.05)10=0.614

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:

ParticularsAmount ($)
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 (a)×(b)61,400

(Table 1)

(2)

Calculate stated semiannual interest rate:

Semiannual stated interest rate=Stated interest rate2= 10%2= 5% (3)

Calculate the interest payable:

Interest payable=Face value of bonds×Semiannual interest rate=$100,000×5100=$5,000 (4)

Calculate the present value factor for semiannual market of 5% for 10 periods:

Present Value of  Annuity factor= 1(1+i)ni=1(1+0.05)105%=7.722 (5)

Calculate present value of interest payments:

ParticularsAmount ($)
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 (a)×(b)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.

Issue price of bonds={Present value of principal (8)+Present value of interest payments (10)}=$67,600+$40,555=$108,155

Therefore, the issue price of the bonds is $108,155.

Working notes:

Calculate the present value for 5 periods and 8% interest compounded semiannually:

Present Value = 1(1+i)n=1(1+0.04)10=0.676

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:

ParticularsAmount ($)
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 (a)×(b)67,600

(Table 3)

(8)

Calculate the present value factor for semiannual market of 4% for 10 periods:

Present Value of  Annuity factor= 1(1+i)ni=1(1+0.04)104%=8.111 (9)

Calculate present value of interest payments:

ParticularsAmount ($)
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 (a)×(b)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.

Issue price of bonds={Present value of principal (12)+Present value of interest payments (14)}=$55,800+$36,800=$92,600

Therefore, the issue price of the bonds is $92,600.

Working notes:

Calculate the present value for 5 periods and 12% interest compounded semiannually:

Present Value = 1(1+i)n=1(1+0.06)10=0.558

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:

ParticularsAmount ($)
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 (a)×(b)55,800

(Table 5)

(12)

Calculate the present value factor for semiannual market of 6% for 10 periods:

Present Value of  Annuity factor= 1(1+i)ni=1(1+0.06)106%=7.360 (13)

Calculate present value of interest payments:

ParticularsAmount ($)
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 (a)×(b)36,800

(Table 6)

(14)

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Chapter 10 Solutions

Financial Accounting for Undergraduates

Ch. 10 - Prob. 11SSQCh. 10 - Prob. 1QCh. 10 - Prob. 2QCh. 10 - Prob. 3QCh. 10 - Prob. 4QCh. 10 - Prob. 5QCh. 10 - Prob. 6QCh. 10 - Prob. 7QCh. 10 - Prob. 8QCh. 10 - Prob. 9QCh. 10 - Prob. 10QCh. 10 - Prob. 11QCh. 10 - Prob. 12QCh. 10 - Prob. 13QCh. 10 - Prob. 14QCh. 10 - Prob. 15QCh. 10 - Prob. 16QCh. 10 - Prob. 17QCh. 10 - Prob. 18QCh. 10 - Prob. 19QCh. 10 - Prob. 1SECh. 10 - Prob. 2SECh. 10 - Prob. 3SECh. 10 - Prob. 4SECh. 10 - Prob. 5SECh. 10 - Prob. 6SECh. 10 - Prob. 7SECh. 10 - Prob. 8SECh. 10 - Prob. 9SECh. 10 - Prob. 10SECh. 10 - Prob. 1AECh. 10 - Prob. 2AECh. 10 - Prob. 3AECh. 10 - Prob. 4AECh. 10 - Prob. 5AECh. 10 - Prob. 6AECh. 10 - Prob. 7AECh. 10 - Prob. 8AECh. 10 - Prob. 9AECh. 10 - Prob. 10AECh. 10 - Prob. 11AECh. 10 - Prob. 12AECh. 10 - Prob. 13AECh. 10 - Prob. 14AECh. 10 - Prob. 15AECh. 10 - Prob. 16AECh. 10 - Prob. 17AECh. 10 - Prob. 1BECh. 10 - Prob. 2BECh. 10 - Prob. 3BECh. 10 - Prob. 4BECh. 10 - Prob. 5BECh. 10 - Prob. 6BECh. 10 - Prob. 7BECh. 10 - Prob. 8BECh. 10 - Prob. 9BECh. 10 - Prob. 10BECh. 10 - Prob. 11BECh. 10 - Prob. 12BECh. 10 - Prob. 13BECh. 10 - Prob. 14BECh. 10 - Prob. 15BECh. 10 - Prob. 16BECh. 10 - Prob. 17BECh. 10 - Prob. 1APCh. 10 - Prob. 2APCh. 10 - Prob. 3APCh. 10 - Prob. 4APCh. 10 - Prob. 5APCh. 10 - Prob. 6APCh. 10 - Prob. 7APCh. 10 - Prob. 8APCh. 10 - Prob. 9APCh. 10 - Prob. 10APCh. 10 - Prob. 1BPCh. 10 - Prob. 2BPCh. 10 - Prob. 3BPCh. 10 - Prob. 4BPCh. 10 - Prob. 5BPCh. 10 - Prob. 6BPCh. 10 - Prob. 7BPCh. 10 - Prob. 8BPCh. 10 - Prob. 9BPCh. 10 - Prob. 10BPCh. 10 - Prob. 10SPCh. 10 - Prob. 1EYKCh. 10 - Prob. 2EYKCh. 10 - Prob. 3EYKCh. 10 - Prob. 4EYKCh. 10 - Prob. 5EYKCh. 10 - Prob. 6EYKCh. 10 - Prob. 7EYKCh. 10 - Prob. 8EYKCh. 10 - Prob. 9EYKCh. 10 - Prob. 10EYKCh. 10 - Prob. 11EYK
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