Question

1. A proposed cost-saving project requires a device with an installed cost of $540,000. The project will last for five years. The device has a CCA rate of 20%. The required initial net working capital investment is $20,000, the marginal tax rate is 37%, and the required return on the project is 11%. The device has an estimated salvage value of $95,000 at the end of Year 5, and the net working capital investment will also be recovered at the end of Year 5. What level of pre-tax cost savings do we require for this project to be profitable?                                                     (10 marks)

Answer 1

The NPV of this project can be calculated as:

NPV = -initial cost + Present Value (PV) of after-tax cost savings + PV of salvage value + PV of future CCA tax shields (assuming the equipment lasts forever) + Tax shield adjustment (since equipment has a finite life of 5 years)

CCA schedule (using the half-year rule):

Formula	Year (n)	0	1	2	3	4	5
UCCn-1 - CCAn	UCC	540,000	486,000	388,800	311,040	248,832	199,065.60
CCA1 = d*C/2; other years CCA = d*UCCn -1	CCA		54,000	97,200	77,760	62,208	49,766.40

For the project to be profitable, the NPV has to break even which means the NPV has to be zero. Assuming that cost savings each year are same, the cost savings at which NPV = 0 can be found using Solver, as follows:

A 3 Given data 4 Initial investment (C) 5 CCA rate (d) 6 Working capital requirement (WC) 7 Salvage value (SV) 8 Life(n) 9 Tax rate (T) 10 Required return (k) 11 Cost savings per year (Cs) 540000 20% 20000 95000 37% 11% 164358.5 13 Calculations: 14 Formula 15 -540000.00 16 -WC + WC/(1+k)^n 17 Sv/(1+k)^n 18 (d*c*T/(k+d) *[(1 +0.5k)/(1+k)] 19 -[1/(1+k)^n]*[d*SV*T/(k+d)] 20 Using PV function: PV(k, n, Cs*(1-T)) 21 Sum of all PVS Outflow Initial investment PV of working capital Outflow requirement Inflow PV of salvage value Inflow PV of CCA tax shield Outflow Tax shield adjustment Inflow PV of after-tax cost savings NPV -8130.97 56377.88 122516.13 -13457.94 382694.91 0.00

The pre-tax cost savings at which this project will start to be profitable is $164,358.54 per year.

(Note: The NPV formula is only for those cases where the salvage value is less than the book value of the equipment at the end of its life.)