A3_Soln

# A3_Soln - ACTSC 371 — Assignment #3 Solutions 8.10...

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Unformatted text preview: ACTSC 371 — Assignment #3 Solutions 8.10 Initial revenues = \$2.5 x 2,000,000 = \$5,000,000 Initial expenses = \$0.7 x 2,000,000 = \$1,400,000 PV after tax = \$5,000,000 (1 - 0.4) / (0.10 - 0.07) — \$1,400,000 (1 — 0.4) r (0.10 - 0.05) = \$100,000,000 - \$16,300,000 = \$83,200,000 8.11 The analysis of the NPV of this project is most easily accomplished by separating the CCA costs from the project's other cash flows. The CCA costs are in nominal terms. Those costs should be discounted at a riskless rate. The riskless nominal rate is given. The revenues and variable costs are given in nominal terms, but their growth rates are real growth rates. Hence, they are most easily discounted using the real rate for risky cash ﬂows. Remember, you can use different types of discount rates (real vs. nominal) in a problem as long as you are careful to discount real cash ﬂows with the real rate and nominal cash flows with the nominal rate. First, determine the net income from the revenues and expenses not including CCA. Note, the nominal price of a buckeye during the ﬁrst year was \$3.15. The inﬂation rate during the period was 5%. Therefore, the real price of a buckeye was \$3.00 (\$3 .15/1 .05). Similarly, the nominal variable cost for a buckeye was \$02625; the real variable cost is \$0.25 (\$0.2625/l .05). — t=4 (1,283,029) -—_— 19.0467619%* * Since these cash ﬂows are in real terms, you must use the real discount rate to ﬁnd the PV of the ﬂows. Real discount rate = [125/105] —1 = 019047619 = 19.047619% The PV of the annual net incomes using the real discount rate is \$5,709,740. The NPV of the project is the present value of the net income in each year plus, the present value of the CCA tax shield. PV of CCA TS = (Cd Tc / k+cl) [1+.5k/(1+k)] w(Sch/k+d) [l/(l+k)“] : [(5,000,000 x20 x.40)/(.20+.20)] (1 . 10/1 .20) — [(638,140.78 x .20 x .40)/(.20+.20)] (1/125) 8.17 : \$1,1,000,000 - \$51,291 = \$1,048,709 Again, the CCA tax Shield is in nominal terms, so discount it using the nominal riskless rate. NPV = -\$6,000,000 + \$5,709,740 + \$1,048,709 = \$758,449. Note that International Buckeyes will continue the CCA pool by replacing the plant so there are no further tax implications for the sale of the equipment. 1) In nominal terms you could receive, one year from now, after-tax \$10,540 (\$10,000 + 10,000 x 0.09 x.60) which is \$10,135 in real terms (\$10,540/1.04). Real interest rate = (1.09/104) - 1 = 4.8077% 2) In nominal terms you would receive \$10,300 after-tax (\$10,000 + 10,000 x05 x.60) but only \$10,198 in real terms. Real interest rate = (1.05/1 .01) —1 = 3.96% The second alternative is better since you would have more purchasing power at the end of the year. This illustrates how inﬂation is a hidden tax. 1-. 505 oz 35:. SEE ESQ \$8 EOE OZ E05 oz 5:5: o; n Eon \$31 uoow mm atom 039” ﬁnc— uoob comﬂuuw 225m #65 9% x E: a; x :8 x :5: E05 m BEE 2:95 032: woom m Eco .25 332: BE m.va Em £35m uoom bso 35m .25an mm £35 039: we ax; Sm EBB 332:6. .25an 05 :83 96: 230% two md B-IOS 9.7 Using the formula for accounting proﬁt break even with CCA: Fixed cos ts(1 —Tc) + EACP Breakeven = ________H__V_CCAIS__ (Saleprt'ce ~— variable cos ts)((1 — TC) (1, 500 \$1,100)(1—.35) Breakeven = 98’ 000 = 376.92units The company will have to sell 377 units to break even. * Qﬁf‘rj 1 HQ) t . 4+3? ﬁbﬁfi has I u M _________ _. _ =~ " ‘ ‘ t ,1; ‘ -: PU 4" V M ‘ h k h. m, ﬁg ‘ w _ u ,. _ Eh _____.3fz‘i :— 5‘61 _“7___'_'"}‘E.__§Lﬁm m 33“ =-=: ______ ‘ _ = _, L j. “a; 3.737“ _____ .‘ _, W—_ I“ W _ M {£53 m [5. 4L. Jz’img _ 43a 5% HES /£}W- _. m WJfSZJllékggéﬁCgﬁﬁmﬁ7iﬂm H75ng -‘- ﬂag as; 7: “57227; 252 :mmjmu:,fmi;:immﬁﬁ@35:_wg:if ...
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## This note was uploaded on 04/27/2010 for the course ACTSC 371 taught by Professor Wood during the Spring '08 term at Waterloo.

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A3_Soln - ACTSC 371 — Assignment #3 Solutions 8.10...

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The provided text appears to be a set of solutions to problems from an assignment in a financial mathematics or corporate finance course. It contains multiple questions and their corresponding solutions, primarily involving calculations of present values, net present values, and break-even points.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
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First, describe the content structure you found in 1-2 sentences.

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A3_Soln

# A3_Soln - ACTSC 371 — Assignment #3 Solutions 8.10...

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Unformatted text preview: ACTSC 371 — Assignment #3 Solutions 8.10 Initial revenues = \$2.5 x 2,000,000 = \$5,000,000 Initial expenses = \$0.7 x 2,000,000 = \$1,400,000 PV after tax = \$5,000,000 (1 - 0.4) / (0.10 - 0.07) — \$1,400,000 (1 — 0.4) r (0.10 - 0.05) = \$100,000,000 - \$16,300,000 = \$83,200,000 8.11 The analysis of the NPV of this project is most easily accomplished by separating the CCA costs from the project's other cash flows. The CCA costs are in nominal terms. Those costs should be discounted at a riskless rate. The riskless nominal rate is given. The revenues and variable costs are given in nominal terms, but their growth rates are real growth rates. Hence, they are most easily discounted using the real rate for risky cash ﬂows. Remember, you can use different types of discount rates (real vs. nominal) in a problem as long as you are careful to discount real cash ﬂows with the real rate and nominal cash flows with the nominal rate. First, determine the net income from the revenues and expenses not including CCA. Note, the nominal price of a buckeye during the ﬁrst year was \$3.15. The inﬂation rate during the period was 5%. Therefore, the real price of a buckeye was \$3.00 (\$3 .15/1 .05). Similarly, the nominal variable cost for a buckeye was \$02625; the real variable cost is \$0.25 (\$0.2625/l .05). — t=4 (1,283,029) -—_— 19.0467619%* * Since these cash ﬂows are in real terms, you must use the real discount rate to ﬁnd the PV of the ﬂows. Real discount rate = [125/105] —1 = 019047619 = 19.047619% The PV of the annual net incomes using the real discount rate is \$5,709,740. The NPV of the project is the present value of the net income in each year plus, the present value of the CCA tax shield. PV of CCA TS = (Cd Tc / k+cl) [1+.5k/(1+k)] w(Sch/k+d) [l/(l+k)“] : [(5,000,000 x20 x.40)/(.20+.20)] (1 . 10/1 .20) — [(638,140.78 x .20 x .40)/(.20+.20)] (1/125) 8.17 : \$1,1,000,000 - \$51,291 = \$1,048,709 Again, the CCA tax Shield is in nominal terms, so discount it using the nominal riskless rate. NPV = -\$6,000,000 + \$5,709,740 + \$1,048,709 = \$758,449. Note that International Buckeyes will continue the CCA pool by replacing the plant so there are no further tax implications for the sale of the equipment. 1) In nominal terms you could receive, one year from now, after-tax \$10,540 (\$10,000 + 10,000 x 0.09 x.60) which is \$10,135 in real terms (\$10,540/1.04). Real interest rate = (1.09/104) - 1 = 4.8077% 2) In nominal terms you would receive \$10,300 after-tax (\$10,000 + 10,000 x05 x.60) but only \$10,198 in real terms. Real interest rate = (1.05/1 .01) —1 = 3.96% The second alternative is better since you would have more purchasing power at the end of the year. This illustrates how inﬂation is a hidden tax. 1-. 505 oz 35:. SEE ESQ \$8 EOE OZ E05 oz 5:5: o; n Eon \$31 uoow mm atom 039” ﬁnc— uoob comﬂuuw 225m #65 9% x E: a; x :8 x :5: E05 m BEE 2:95 032: woom m Eco .25 332: BE m.va Em £35m uoom bso 35m .25an mm £35 039: we ax; Sm EBB 332:6. .25an 05 :83 96: 230% two md B-IOS 9.7 Using the formula for accounting proﬁt break even with CCA: Fixed cos ts(1 —Tc) + EACP Breakeven = ________H__V_CCAIS__ (Saleprt'ce ~— variable cos ts)((1 — TC) (1, 500 \$1,100)(1—.35) Breakeven = 98’ 000 = 376.92units The company will have to sell 377 units to break even. * Qﬁf‘rj 1 HQ) t . 4+3? ﬁbﬁfi has I u M _________ _. _ =~ " ‘ ‘ t ,1; ‘ -: PU 4" V M ‘ h k h. m, ﬁg ‘ w _ u ,. _ Eh _____.3fz‘i :— 5‘61 _“7___'_'"}‘E.__§Lﬁm m 33“ =-=: ______ ‘ _ = _, L j. “a; 3.737“ _____ .‘ _, W—_ I“ W _ M {£53 m [5. 4L. Jz’img _ 43a 5% HES /£}W- _. m WJfSZJllékggéﬁCgﬁﬁmﬁ7iﬂm H75ng -‘- ﬂag as; 7: “57227; 252 :mmjmu:,fmi;:immﬁﬁ@35:_wg:if ...
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## This note was uploaded on 04/27/2010 for the course ACTSC 371 taught by Professor Wood during the Spring '08 term at Waterloo.

### Page1 / 7

A3_Soln - ACTSC 371 — Assignment #3 Solutions 8.10...

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The provided text appears to be a set of solutions to problems from an assignment in a financial mathematics or corporate finance course. It contains multiple questions and their corresponding solutions, primarily involving calculations of present values, net present values, and break-even points.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS