Question

Please answer b-h

Choo Choo Inc. is a manufacturer of model trains. The company is considering the purchase of an industrial 3D printer, which will allow the firm to produce custom-made model trains for its high-end customers. The printer will cost $2,500,000, and it is expected to produce net cash flows of $600,000 per year for the next six years. Liquidation of the equipment will net the firm $350,000 in cash at the end of six years. The firm requires a 15% rate of return on all investments. Ignore the effects of taxes.

a. What is the payback period for the proposed investment in the 3D printer? Provide your answer in number of years and months.

b. What is the printer’s discounted payback period? Provide your answer in number of years and months.

c. Choo Choo’s cutoff period is set at five years. Based on the payback period investment criterion, will the company purchase the printer? Will it purchase the printer based on the discounted payback period investment criterion?

d. What is the printer’s net present value (NPV)? Should the company purchase the printer based on the NPV investment criterion?

e. What is the printer’s profitability index (PI)? Should the company purchase the printer based on the PI investment criterion?

f.   What is the printer’s internal rate of return (IRR)?

Answer 1

(a ): Pay back period= 4 years and 2 months

(b ): Discounted pay back period: Will not payback during the project period of 6 years based on discounted pay back.

Calculation of pay back and discounted pay back as follows:

00 А B C E F 1 Pay back period 2 Discount rate (r )= 15% 3 Project cost in year 0 2,500,000 4 All amounts in $ 5 Given values Present Value Cumulative Cumulative Present 6 Year (t) Cash flow (C) Investment Formula Value Worth 7 0 (2,500,000) (2,500,000) (2,500,000.00) (2,500,000.00) 1 600,000 (1,900,000) C/(1+r) 521,739.13 (1,978,260.87) 9 2 600,000 (1,300,000) C/(1+r)^2 453,686.20 (1,524,574.67) 10 3 600,000 (700,000) C/(1+r)^3 394,509.74 (1,130,064.93) 11 4 600,000 (100,000) C/(1+r)^4 343,051.95 (787,012.98) 12 600,000 500,000 C/(1+r)^5 298,306.04 (488,706.94) 950,000 1,450,000 C/(1+r)^5 410,711.22 (77,995.73) 14 15 16 Pay back period Ordinary Discounted 17 Last whole year of recovery 4 18 Balance after last whole year of recovery 100,000 19 Next year recovery 600,000 20 Fraction of pay back year D18/D19 0.166667 F18/F19 21 Total pay back period years D17+D20 4.166667 F17+F20 22 4 years and 0.166667*12= 2 months. 5 6 3

(c ): Based on pay back period, can purchase the printer since cut off period is 5 years while pay back is lower at 4 years and 2 months.

Cannot purchase based on discounted pay back criterion.

(d ): Net Present Value= $ -77,995.73 (Negative)

The company will not purchase the printer based on NPV criterion since NPV is negative.

(e ): Profitability Index (PI)= 0.97

The company will not purchase the printer based on PI criterion since PI is less than 1.

(f ): Internal Rate of Return (IRR) = 13.898638%

Calculation of NPV, PI and IRR as below:

N 1 F15 f =IRR(E5:E11) А B C D E F 1 Discount Rate = 15% Year Disc rate PV Factor Cash Flow PV 3 1/(1+r)^t 4 (t) PVIF (CF) (CF*PVIF) 5 Initial Investment 0 -$2,500,000 6 Cash flows 15% 0.869565 $600,000 521739.13 7 Cash flows 2 15% 0.756144 $600,000 453686.20 8 Cash flows 3 15% 0.657516 $600,000 394509.74 9 Cash flows 4 15% 0.571753 $600,000 343051.95 10 Cash flows 5 15% 0.497177 $600,000 298306.04 11 Cash flows 6 15% 0.432328 $950,000 410711.22 12 Sum of PVs of positive cash flow 2422004.27 13 NPV=Sum of PVs less initial inivestment = F12-E5*-1 $ (77,995.73) 14 Profitability index = Sum of PVs/Initial Investment=(F12/E5*-1) 0.97 15 IRR = IRR(E5:E11) 13.898638% www