Joan, the project manager, asks you to evaluate alter­natives A and B on the basis of their PW values using a real interest rate of 10% per year and an inflation rate of 3% per year (a) without any adjustment for infla­tion, and (b) with inflation considered. Also, write the spreadsheet functions that will display the correct PW values. (c) Joan clearly wants alternative A to be se­lected. If inflation is steady at 3% per year, what real return i would machine A have to generate each year to make the choice between A and B indifferent? What is the required return with inflation considered?

Question

Answer 1

(a) PWA = -31,000 – 28,000(P/A,10%,5) + 5000(P/F,10%,5)

= -31,000 – 28,000(3.7908) + 5000(0.6209)

= $-134,038



PWB = -48,000 – 19,000(P/A,10%,5) + 7000(P/F,10%,5)

= -48,000 – 19,000(3.7908) + 7000(0.6209)

= $-115,679



Select machine B



Spreadsheet function for PWA: = - PV(10%,5,-28000,5000) - 31000

PWB: = - PV(10%,5,-19000,7000) - 48000

(b) if = 0.10 + 0.03 + (0.10)(0.03) = 0.133 (13.3%)



PWA = -31,000 – 28,000(P/A,13.3%,5) + 5000(P/F,13.3%,5)

= -31,000 – 28,000(3.4916) + 5000(0.5356)

= $-126,087



PWB = -48,000 – 19,000(P/A,13.3%,5) + 7000(P/F,13.3%,5)

= -48,000 – 19,000(3.4916) + 7000(0.5356)

= $-110,591



Select machine B



Spreadsheet function for PWA: = - PV(13.3%,5,-28000,5000) - 31000

PWB: = - PV(13.3%,5,-19000,7000) – 48000



(b) Maintain i = 10% for B; use Goal Seek to force PW difference to be 0 while changing the i for A (cell F2).

A real i of 17.7% and an inflation-adjusted return of 21.2% are required for breakeven.