Engineering Economy
Engineering Economy
8th Edition
ISBN: 9780073523439
Author: Leland T Blank Professor Emeritus, Anthony Tarquin
Publisher: McGraw-Hill Education
Question
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Chapter 10, Problem 27P

(a):

To determine

Calculate the face value.

(a):

Expert Solution
Check Mark

Explanation of Solution

Debt capital (D) is $2,500,000. Required return (RR) is $2,500,000. Selling is at 12th year. Returns from the bond (r) is 4.2%. Discount rate (i) is 3% quarterly on the face value. Effective tax rate (ET) is 35%.

Face value (F) of the bond that would give $2,500,000 can be calculated as follows:

F=RR1i=2,500,00010.03=2,500,0000.97=2,577,319.59

The face value to obtain $2,500,000 million return is $2,577,319.59.

(b):

To determine

Cost of debt capital after effective tax rate.

(b):

Expert Solution
Check Mark

Explanation of Solution

Debt capital (D) is $2,500,000. Time period (n) is 20. Returns from the bond (r) is 4.2%. Discount rate (i) is 3% quarterly on the face value. Effective tax rate (ET) is 35%. Number of quarter in a year (Q) is 4. The cost of debt capital (i) can be calculated as follows:

D=F×rQ×(1ET)((1+i)n×Q1i(1+i)n×Q)F(1+i)n×Q2,500,000=2,577,319.59×0.0424×(10.35)((1+i)20×41i(1+i)20×4)2,577,319.59(1+i)20×42,500,000=27,061.86×(0.65)((1+i)801i(1+i)80)2,577,319.59(1+i)80

Substitute i as 0.7% by trial and error method in the above calculation.

2,500,000=27,061.86×(0.65)((1+0.007)8010.007(1+0.007)80)+2,577,319.59(1+0.007)802,500,000=17,590.21(1.7472610.007(1.74726))+2,577,319.591.747262,500,000=17,590.21(0.747260.01223)+1,475,063.582,500,000=17,590.21(61.10057)+1,475,063.582,500,000=1,074,771.86+1,475,063.582,500,000<2,549,835.44

Since the calculated value is greater than the present value of quarterly debt value, increase the i to 0.734%.

2,500,000=27,061.86×(0.65)((1+0.00734)8010.00734(1+0.00734)80)+2,577,319.59(1+0.00734)802,500,000=17,590.21(1.79509110.00734(1.795091))+2,577,319.591.7950912,500,000=17,590.21(0.7950910.013176)+1,435,759.852,500,000=17,590.21(60.343883)+1,435,759.852,500,0002,497,221.42

The calculated value is nearly equal to the present value of quarterly debt value. Thus, the cost of debt capital is 0.743% per quarter. Thus, the annual cost of debt is 2.936%(0.734×4).

The spreadsheet function to calculate the cost of debt capital is given below:

= RATE(80,-17590,2500000,-2577320)*4

The above function gives the value of 2.93%.

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