(a):
Calculate cost of debt capital before tax.
(a):
Explanation of Solution
Interest expense (IP) is $1,200,000 per year. Initial received payment (RP) is $19,000,000. Face
RP=IP((1+i)n−1i(1+i)n)+B(1+i)n19,000,000=1,200,000((1+i)15−1i(1+i)15)+20,000,000(1+i)15
Substitute i as 6% by trial and error method in the above calculation.
19,000,000=1,200,000((1+0.06)15−10.06(1+0.06)15)+20,000,000(1+0.06)1519,000,000=1,200,000(2.396558−10.06(2.396558))+20,000,0002.39655819,000,000=1,200,000(1.3965580.143793)+8,345,301.8919,000,000=1,200,000(9.712281)+8,345,301.8919,000,000=11,654,737.2+8,345,301.8919,000,000=20,000,039.09
Since the calculated value is greater than the initial received payment, increase the cost of capital from 6% to 6.53%.
19,000,000=1,200,000((1+0.0653)15−10.0653(1+0.0653)15)+20,000,000(1+0.0653)1519,000,000=1,200,000(2.582729−10.0653(2.582729))+20,000,0002.58272919,000,000=1,200,000(9.384585)+7,743,747.0219,000,000=11,261,502+7,743,747.0219,000,000≈19,005,249.02
The calculated value is equal to the initial received payment. Thus, it is confirmed that the cost of debt capital is 6.53%.
(b):
Calculate cost of debt capital after tax.
(b):
Explanation of Solution
Effective tax rate (ET) is 29%. Cost of capital (i) before tax can be calculated as follows:
RP=(IP−(IP×ET))((1+i)n−1i(1+i)n)+B(1+i)n19,000,000=(1,200,000−(1,200,000×0.29))((1+i)15−1i(1+i)15)+20,000,000(1+i)1519,000,000=(1,200,000−348,000)((1+i)15−1i(1+i)15)+20,000,000(1+i)1519,000,000=852,000((1+i)15−1i(1+i)15)+20,000,000(1+i)15
Substitute i as 5% by trial and error method in the above calculation.
19,000,000=852,000((1+0.05)15−10.05(1+0.05)15)+20,000,000(1+0.05)1519,000,000=852,000(2.078928−10.05(2.078928))+20,000,0002.07892819,000,000=852,000(1.0789280.103946)+9,620,342.7919,000,000=852,000(10.379697)+9,620,342.7919,000,000=8,843,502.696+9,620,342.7919,000,000>18,463,845.49
Since the calculated value is less than the initial received payment, decrease the cost of capital from 5% to 4.73%.
19,000,000=852,000((1+0.0473)15−10.0473(1+0.0473)15)+20,000,000(1+0.0473)1519,000,000=852,000(2.000168−10.0473(2.000168))+20,000,0002.00016819,000,000=852,000(1.0001680.094608)+9,999,160.0719,000,000=852,000(10.571706)+9,999,160.0719,000,000=9,007,093.51+9,999,160.0719,000,000≈19,006,253.58
The calculated value is equal to the initial received payment. Thus, it is confirmed that the cost of debt capital is 4.73%.
(c):
Spreadsheet function.
(c):
Explanation of Solution
Spreadsheet function for cost of debt capital before tax is given below.
= RATE(15,-1200000,19000000,-20000000)
Spreadsheet function for cost of debt capital after tax is given below.
= RATE(15,-1200000*(1-0.29),19000000,-20000000)
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Chapter 10 Solutions
Engineering Economy
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