The Tre Manufacturing Company is currently earning an average before-tax return

Question

The Tre Manufacturing Company is currently earning an average before-tax return of 25% on its total investment. The board of directors of the tire manufacturing company is considering three proposals as given in the table below. 6. Cash Flows End of YearProposal A Proposal B Proposal c $40 000 18 000 18 000 18 000 18 000 $60 000 25 00O 25 000 25 000 25 000 $50 000 27 000 27 000 27 000 27 00o 2 3 Proposal A is for a new system of conveyors that will replace the existing conveyors; the conveyors are vital to the tire's production. Proposal B is for a plant expansion. Proposal C is for implementing a new product line of light truek tires. There is a high probability that this product could fail in the marketplace, resulting in the loss of most of the S50 000 initial investments. The board feels that they would need at least a 40% rate of return on this project to compensate for its additional riskiness. Which of these three proposals are acceptable by comparing the NPV? a. A b, B ?.?

Explanation / Answer

IRR = R1+(NPV1*(R2-R1))/(NPV1-NPV2)
R1 is lower discount rate
R2 is higher discount rate
NPV1 is net present value at R1
NPV2 is net present value at R2
So, we need to find R1 and R2 at which IRR become zero or negative
NPV = CF0+CFn/(1+i)^n
IRR for A
NPV1=(-40000/(1+0.25)^0)+(18000/(1+0.25)^1)+(18000/(1+0.25)^2)+(18000/(1+0.25)^3)+(18000/(1+0.25)^4)=2508.8
NPV2=(-40000/(1+0.30)^0)+(18000/(1+0.30)^1)+(18000/(1+0.30)^2)+(18000/(1+0.30)^3)+ (18000/(1+0.30)^4)=-1007.68
IRR for A = 0.25+(2508.8*(0.30-0.25))/(2508.8+1007.68) = 0.2856 =28.56 per cent
IRR for B
NPV1=(-60000/(1+0.20)^0)+(25000/(1+0.20)^1)+(25000/(1+0.20)^2)+(25000/(1+0.20)^3)+ (25000/(1+0.20)^4)=4718.36
NPV2=(-60000/(1+0.25)^0)+(25000/(1+0.25)^1)+(25000/(1+0.25)^2)+(25000/(1+0.25)^3)+ (25000/(1+0.25)^4)=-960
IRR for B = 0.20+(4718.36*(0.25-0.20))/(4718.36+960) = 0.2415 =24.15 per cent
IRR for C
NPV1=(-50000/(1+0.35)^0)+(27000/(1+0.35)^1)+(27000/(1+0.35)^2)+(27000/(1+0.35)^3)+ (27000/(1+0.35)^4) = 3917.59
NPV2=(-50000/(1+0.42)^0)+(27000/(1+0.42)^1)+(27000/(1+0.42)^2)+(27000/(1+0.42)^3)+ (27000/(1+0.42)^4) = -1525.35
IRR for C = 0.35+(3917.59*(0.42-0.35))/(3917.59+1525.35) = 0.4003 =40 per cent

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