Question

Delta Widget Corp. (DWC) is considering whether to purchase a new widget-producing machine at a cost of $900,000. The machine would produce 100,000 widgets per year during its useful life of three years, and would be depreciated for tax purposes at a rate of $300,000 per year. No salvage value is expected. Currently, widget prices are $15. The materials and labor required to produce a widget cost $9. The inflation rate is expected to be 3% per year, and the prices of both widgets and widget inputs are expected to increase at the inflation rate. The tax rate is 34%. (a) Given the relatively low risks of producing for the widget market, DWC management believes that a 4% real discount rate is appropriate. What nominal discount rate should be used? (b)Compute the net nominal post-tax cash flows resulting from the purchase of a widget machine on a year-by-year basis. Assume that all cash flows except the initial $900,000 investment occur at year-end. (c) Compute the NPV of the widget machine. Identify whether each of the following would increase or decrease the NPV of the widget machine, and briefly explain why – no computations are required : (d) An increase in the real discount rate. (e) An increase in the projected inflation rate. (f) A revised forecast where widget prices increase at a slower rate than the general inflation rate.  

Answer 1

a)

Nominal Discount Rate = (1 + Real Discount Rate)(1 + Inflation Rate) – 1

Nominal Discount Rate = (1+4%)*(1+3%)-1 = 0.0712 = 7.12%

b)

Year 0 CF= -$900,000

Year 1 Post tax CF= EBIT(1-t) + Dep

= (Number of units sold *(Selling Price - Cost Price) - Dep )*(1-t) + Dep

= [100,000 (15-9) - 300,000 ] + 300,000

= $498,000

Year 2 Post tax CF= EBIT(1-t) + Dep

Selling Price for year 2 = selling price year 1*(1+Inflation) = 15*(1+0.04) = 15.45

Cost Price for year 2 = Cost price year 1*(1+Inflation) = 9*(1+0.04) = 9.27

= (Number of units sold *(Selling Price - Cost Price) - Dep )*(1-t) + Dep

= [100,000 (15.45-9.27) - 300,000 ] + 300,000

= $509,880

Year 3 Post tax CF= EBIT(1-t) + Dep

Selling Price for year 3 = selling price year 2*(1+Inflation) = 15.45*(1+0.04) = 15.91

Cost Price for year 3 = Cost price year 2*(1+Inflation) = 9.27*(1+0.04) = 9.55

= (Number of units sold *(Selling Price - Cost Price) - Dep )*(1-t) + Dep

= [100,000 (15.91-9.55) - 300,000 ] + 300,000

= $522,116

c)

NPV = - initial Cost + CF1 / (1+r)¹ + CF2 / (1+r)²  + CF3 / (1+r)³

NPV = -900,000 + 498,000 / (1+0.0712) + 509,880/ (1+0.0712)² + 522,116 / (1+0.0712)³

NPV = $434,023

d) if real discount rate is increased, nominal discount rate will increase . Since discount rate is in denominator for NPV calculation, increase in rate will decrease the NPV

e) if inflation rate is increased, nominal discount rate will increase . Since discount rate is in denominator for NPV calculation, increase in rate will decrease the NPV

f) This will also decrease NPV since price increase is lower than general inflation. So net profit will decrease