EBK ENGINEERING ECONOMY
EBK ENGINEERING ECONOMY
8th Edition
ISBN: 8220103675437
Author: Blank
Publisher: YUZU
Question
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Chapter 10, Problem 26P

(a):

To determine

Calculate cost of debt.

(a):

Expert Solution
Check Mark

Explanation of Solution

Borrowing (B) is $800,000. Effective rate (ER) is 8%. Time period (n) is 8 years. Effective tax rate (ET) is 40%. Cost of debt (i) can be calculated as follows:

B(i(1+i)n(1+i)n1)=(B(i(1+ER)n(1+ER)n1)Bn)(B(i(1+ER)n(1+ER)n1)Bn)ET+Bn800,000(i(1+i)8(1+i)81)=((800,000(0.08(1+0.08)8(1+0.08)81)800,0008)(800,000(0.08(1+0.08)8(1+0.08)81)800,0008)0.4+800,0008)800,000(i(1+i)8(1+i)81)=((800,000(0.08(1.85093)1.850931)100,000)(800,000(0.08(1.85093)1.850931)100,000)0.4+100,000)800,000(i(1+i)8(1+i)81)=((800,000(0.148070.85093)100,000)(800,000(0.148070.85093)100,000)0.4+100,000)800,000(i(1+i)8(1+i)81)=((800,000(0.17401)100,000)(800,000(0.17401)100,000)0.4+100,000)800,000(i(1+i)8(1+i)81)=((139,208100,000)(139,208100,000)0.4+100,000)800,000(i(1+i)8(1+i)81)=(39,208(39,208)0.4+100,000)800,000(i(1+i)8(1+i)81)=123,524.8

Substitute i as 5% by trial and error method in the above calculation.

800,000(0.05(1+.05)8(1+0.05)81)=123,524.8800,000(0.05(1.477455)1.4774551)=123,524.8800,000(0.0738730.477455)=123,524.8800,000(0.154722)=123,524.8123,777.6>123,524.8

Since the annual value of the borrowing is greater than the calculated value, decrease the cost of capital from 6% to 4.95%.

800,000(0.0495(1+.0495)8(1+0.0495)81)=123,524.8800,000(0.0495(1.471836)1.4718361)=123,524.8800,000(0.0728560.471836)=123,524.8800,000(0.15441)=123,524.8123,528123,524.8

The calculated value is equal to the annual value of the borrowing. Thus, it is confirmed that the cost of debt capital is 4.95%.

Borrowing (B) is $800,000. Time period (n) is 10 years. Effective tax rate (ET) is 40%. Bond rate (BR) is 6%. Cost of debt (i) can be calculated as follows:

B(i(1+i)n(1+i)n1)=(B×BR)(B×BR×ET)+B(i(1+i)n1)800,000(i(1+i)10(1+i)101)=(800,000×0.06)(800,000×0.06×0.4)+800,000(i(1+i)101)800,000(i(1+i)10(1+i)101)=48,00019,200+800,000(i(1+i)101)800,000(i(1+i)10(1+i)101)=28,800+800,000(i(1+i)101)

Substitute i as 4% by trial and error method in the above calculation.

800,000(0.04(1+0.04)10(1+0.04)101)=28,800+800,000(0.04(1+0.04)101)800,000(0.04(1.480244)1.4802441)=28,800+800,000(0.041.4802441)800,000(0.059210.480244)=28,800+800,000(0.040.480244)800,000(0.123291)=28,800+800,000(0.083291)98,632.8=28,800+66,632.898,632.8>95,432.8

Since the annual value of the borrowing is greater than the calculated value, decrease the cost of capital from 4% to 3.6%.

800,000(0.036(1+0.036)10(1+0.036)101)=28,800+800,000(0.036(1+0.036)101)800,000(0.036(1.424287)1.4242871)=28,800+800,000(0.0361.4242871)800,000(0.0512740.424287)=28,800+800,000(0.0360.424287)800,000(0.120847)=28,800+800,000(0.084848)96,677.6=28,800+67,878.496,677.696,678.4

The calculated value is equal to the annual value of the borrowing. Thus, it is confirmed that the cost of debt capital is 3.6%. Thus, bond financing is cheaper than the borrowing from bank.

(b):

To determine

Comparing the cost of capital.

(b):

Expert Solution
Check Mark

Explanation of Solution

Before tax the cost of capital from bond financing is 6%, whereas the cost of capital from bank financing is 8%. Thus, bond financing is cheaper before tax analysis. Thus, the result before tax analysis is the same as the after tax analysis.

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