# FN1 Module 6 Handout 1. Class Examples

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1 Class Examples Example 1 GG Inc. has a project that requires the purchase of capital assets costing \$40,000, and additional raw material inventory of \$2,000. This project would use land previously purchased by the company for \$100,000. An appraisal of the land has indicated that the land could be sold today for \$200,000. Shipping and installation costs (for the capital asset) are \$1,500. GG Inc. estimated that the project would generate annual revenues of \$70,000 and annual costs of \$55,000 for six years at each year end. At the end of the project it is estimated that the capital assets could be sold for \$4,000 and the land could be sold for \$500,000, while the additional inventory that was tied up will be released. The assets are in asset class 9, which has a CCA rate of 30%. The tax rate = 40%, and k = 15%. Assume the asset class will remain open. Based on NPV analysis, determine whether or not GG Inc. should accept this project. Solution: Step 1: Summarize the given information Co = -40,000+1,500 WC = -2,000 Opportunity cost = foregone sale proceeds on land tax on gain CFt ( operating benefits) = (70,000 55,000) * (1-T) PVTS PVTSL Co = 40,000+1,500 d = 30% T = 40% k = 15% Sn = 4,000 N = 6 ECF (ending cash flows) Sn (sale of capital asset for 4,000) no tax effect Sale of land - \$500,000 tax on gain Release of WC 1

2 Step 2: Determine all relevant cash flows discount all cash flows to time 0 Actual Incremental include opportunity costs, ignore sunk costs Nominal After-tax CFo: Asset cost \$40,000+1,500 = 41,500 Opportunity cost \$200,000 (200, ,000)*0.4*1/2 = 180,000 Working capital = 2,000 incremental after tax cash flows (benefits) CFT = (70,000-55,000)*(1-0.4) = 9,000 These cash flows will occur every year at year end, for 6 years. This represents an annuity end, 6 years, discounted at 15 % PV = 34, PVTS PVTSL = Co*d*T (1+0.5k) - Sn*d*T * 1 (d+k) (1+k) (d+k) (1+k) n = (41,500)*0.3*0.4 (1+0.5*0.15-4,000*0.3*0.4 * 1 ( ) (1+0.15) ( ) (1+0.15) 6 = 10, = 9, ECF (ending cash flows) Sn = 4,000 (1.15) 6 Sale of land = 500,000 (500, ,000)*0.4*1/2 (1.15) 6 Release of WC = 2,000 (1.15) 6 2

3 Step 3: Set up your template, and enter the values determined above. CFo (initial cash flows) Co - 41,500 Opportunity Cost -180,000 Working - 2,000 CFt PV Incremental operating benefits + 34,060 PVTS PVTSL + 9,884 ECF (Ending cash flows) PV Salvage + 1,729 PV Sale of Land +181,578 PV Release of Working NPV + 4,616 Step 4: STATE YOUR CONCLUSION GG Inc. should accept this project, as the NPV >0, which translates to increased value for the firm. 3

4 Example 2: ABC Company is evaluating several projects. The firm s tax rate is 35% and the appropriate discount rate is 12%. You have been asked to provide the PVTS PVTSL figures for each of the following proposals. Assume the asset class will stay open. All projects have a 5 year planning horizon. Initial Investment Salvage Value CCA rate Length of 1 40,000 30,000 30% 4 years 2 35,000 25,000 30% 5 years 3 90,000 50,000 30% 6 years Solution: We will be using the formula: Co*d*T * _(1+0.5*k) - Sn*d*T * 1 (d+k) (1+k) (d+k) (1+k) n You will notice that for all of the calculations, some values do not change specifically: d T k We could re-write the equation to isolate the values that change, as follows: Co. * d*t * (1+0.5k) - Sn * d*t * 1 (d+k) (1+k) (d+k) (1+k) n For all of these projects, the values for the terms bolded stay the same these terms are referred to as the PVTS and PVTSL factors. Analyzing each of these projects, once the PVTS and PVTSL factors are determined, becomes much more expedient. PVTS factor: Calculate to 6 decimal places d*t * (1+0.5k) = 0.3*0.35 * 1.06 = (d+k) (1+k) PVTSL factor: Calculate to 6 decimal places d*t = 0.3*0.35 = (d+k)

5 For 1: Co = 40,000 Sn = 30,000 n = 4 PVTS PVTSL = 40,000* ,000 * 0.25 * 1 (1.12) 4 For 2: Co =35,000 Sn = 25,000 n = 5 = 9, , = 4,697.9 PVTS PVTSL = 35,000 * ,000 * 0.25 * 1 (1.12) 5 = 8, , = 4, For 3: Co = 90,000 Sn = 50,000 n = 6 PVTS PVTSL = 90,000 * ,000 * 0.25 * 1 (1.12) 6 = 21, , = 14,

6 Example 3: The analysis of a two division company (DV2) has indicated that the beta of the entire company is The company is 100% equity funded. The company is evaluating a project that has the same type of risk as a one division firm, MLTV. MLTV has a beta of 1.85, and is also 100% equity financed. The current risk free rate is 3% and the market risk premium is 5%. Assume the tax rate is zero. cash flows: Initial investment \$10,000 Incremental benefits \$1,000, forever (perpetuity) Required: 1) Determine the current cost of capital for the firm. 2) Determine the appropriate discount rate to be applied to the project under consideration 3) Should the company pursue this project? Solution: Required 1: WACC = RF + beta * (RM RF) = * (0.05) = 9.75% Required 2: RADR = * (0.05) = 12.25% Required 3: NPV = -10, ,000/.1225 = -1, The company should not pursue this project, because the value of the firm will decrease. Note that if we hadn t used the RADR, the NPV would be: NPV wrong = -10, ,000/.0975 = Note: We cannot use the WACC for the entire company to evaluate this project. The risk of the project is not the same as the risk of the overall firm. 6

7 Payback and Discounted Payback Example 4: A project is under consideration with the following cash flows: Initial investment = -100,000 after tax cash flow benefits = 60,000 life = 5 years CCA = N/A Cost of capital = 10% Payback method: Year Cashflow After-tax incremental Cash Flows PV Factor Cumulative Cash Flows 0 Initial cost \$0 \$0 1 operating benefit \$60,000 \$60,000 2 operating benefit \$60,000 \$120,000 3 operating benefit \$60,000 4 operating benefit \$60,000 5 operating benefit \$60,000 6 operating benefit \$60,000 Payback period = 1.7 years Discounted Payback method: Year Initial cost = \$100,000 AT cash flow benefits = \$60,000 life(years) = 5 Cost of = 10.0% Cashflow After-tax incremental Cash Flows PV Factor Present Value of s Cumulative Cash Flows 0 Initial cost -\$100, \$100,000 -\$100,000 1 operating benefit \$60, \$54,545 -\$45,455 2 operating benefit \$60, \$49,587 \$4,132 3 operating benefit \$60, \$45,079 \$49,211 4 operating benefit \$60, \$40,981 \$90,192 5 operating benefit \$60, \$37,255 \$127,447 6 operating benefit \$60, \$33,868 \$161,316 Payback period = 1.9 years 7

8 Example 5: Consider a firm that has six different capital investment proposals this year. Each project has it s own IRR, NPV, PI and capital cost. Each project has the same risk as the firm as a whole. Assume the firm s cost of capital is 10%. Determine which projects should be chosen based on NPV, IRR, PI assuming no capital rationing. Firm's Cost of = 10.00% Using the NPV decision rule: Firm's Cost of = 10.00% \$9,030,000 \$811,835 8

9 Using the IRR decision rule Firm's Cost of = 10.00% \$9,030,000 \$811,835 Using the PI decision rule: Firm's Cost of = 10.00% \$9,030,000 \$811,835 9

10 Example 6: Consider a firm that has six different capital investment proposals this year. Each project has it s own IRR, NPV, PI and capital cost. Each project has the same risk as the firm as a whole. Assume the firm s cost of capital is 10%. The firm has a capital budget of \$6,000,000. Determine which projects should be chosen based on NPV, IRR, PI Based on NPV decision rule: Firm's Cost of = 10.00% \$5,960,000 \$735,785 Based on IRR decision rule: Firm's Cost of = 10.00% \$5,070,000 \$656,168 10

11 Based on the PI: Firm's Cost of = 10.00% \$5,030,000 \$663,824 11

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