Question

Mmasodwo Enterprice is considering investing in a machine to produce computer keyboards. The price of the machine will be ¢530,000 and its economic life is five years. The machine will be fully depreciated by the straight-line method. The machine will produce 15,000 keyboards each year. The price of each keyboard will be ¢40 in the first year and will increase by 5 percent per year. The production cost per keyboard will be ¢20 in the first year and will increase by 6 percent per year. The project will have an annual fixed cost of ¢75,000 and require an immediate investment of ¢25,000 in net working capital. The corporate tax rate for the company is 34 percent. If the appropriate discount rate is 15 percent, what is the NPV of the investment?

Answer 1

It's easy and convenient to solve this question in excel. Let's start with Year 0 in which we have all cash outflows. We are buying the machine for 530,000 and investing in net working capital 25,000. So total cash outflow in Year 0 = 530,000 + 25,000 = 555,000

Year 1:

Machine will produce 15000 keyboards. Selling price of 1 keyboard = 40, so revenue for Year 1 = 15000 * 40 =600,000

Production cost = 15,000 * 20 = 300,000

Fixed cost = 75,000 (Same for all years)

Depreciation used for machine is straight line, so we will divide cost of machine i.e. 530,000 over 5 years = 530,000/5 = 106,000 each year

Now we will calculate income before tax= Revenue - Production cost - fixed cost - depreciation = 600,000-300,000-75,000-106,000 = 119,000

Tax on this income @34% = 119000 * .34 = 40,460

Net income = Income before tax - tax = 119000-40460 = 78,540

Now as we know Depreciation is a non cash expense, to find the cash flow in 1st year, we will add dep to net income = 78,540 + 106,000 = 184,540

Similarly for Year 2 :

Price of keyboard = 40*1.05 (As price increased by 5%) = 42; Cost of keyboard = 20* 1.06 = 21.2 (Cost increased by 6%)

Revenue = 15000 * 42 =630,000; Production cost = 15,000 * 21.2 = 318,000

Fixed cost = 75,000 and Depreciation =106,000 (Fixed cost and depreciation will be same for all years)

Income before tax= Revenue - Production cost - fixed cost - depreciation = 630,000-318,000-75,000-106,000 = 131,000

Tax on this income @34% = 131000 * .34 = 44,540

Net income = Income before tax - tax = 131000-44540 = 86,460

Cash flow in 2nd year = Net income + depreciation= 86,460 + 106,000 = 192,460

Similarly for Year 3:

Price of keyboard = 42*1.05 (As price increased by 5%) = 44.1; Cost of keyboard = 21.2* 1.06 = 22.47 (Cost increased by 6%)

Revenue = 15000 * 44.1 =661,500; Production cost = 15,000 * 22.47= 337,080

Fixed cost = 75,000 and Depreciation =106,000 (Fixed cost and depreciation will be same for all years)

Income before tax= Revenue - Production cost - fixed cost - depreciation = 661,500-337,080-75,000-106,000 = 143,420

Tax on this income @34% = 143420 * .34 = 48,763

Net income = Income before tax - tax = 143420-48763 = 94,657

Cash flow in 3rd year = Net income + depreciation= 94,657 + 106,000 = 200,657

For Year 4:

Price of keyboard = 44.1*1.05 (As price increased by 5%) = 46.31; Cost of keyboard = 22.47* 1.06 = 23.82 (Cost increased by 6%)

Revenue = 15000 * 46.31 =694,575; Production cost = 15,000 * 23.82= 357,305

Fixed cost = 75,000 and Depreciation =106,000 (Fixed cost and depreciation will be same for all years)

Income before tax= Revenue - Production cost - fixed cost - depreciation = 694,575-357,305-75,000-106,000 = 156,270

Tax on this income @34% = 156270 * .34 = 53,132

Net income = Income before tax - tax = 156270-53132 = 103,138

Cash flow in 4th year = Net income + depreciation= 103,138 + 106,000 = 209,138

For Year 4:

Price of keyboard = 46.31*1.05 (As price increased by 5%) = 48.62; Cost of keyboard = 23.82* 1.06 = 25.25 (Cost increased by 6%)

Revenue = 15000 * 48.62 =729,304; Production cost = 15,000 * 25.25 = 378,743

Fixed cost = 75,000 and Depreciation =106,000 (Fixed cost and depreciation will be same for all years)

Income before tax= Revenue - Production cost - fixed cost - depreciation = 729,304-378,743-75,000-106,000 = 169,561

Tax on this income @34% = 169,561 * .34 = 57,651

Net income = Income before tax - tax = 169561-57651 = 111,910

In 5th year, we also receive the investment which we did in working capital in starting

Cash flow in 5th year = Net income + depreciation + inv. in working capital = 111,910 + 106,000 + 25000 = 242,910

After calculating all cash flows, we will find the present value of these cash flows.

PV of CF₀ = -555,000 (-ve sign because it is an outflow)

PV of CF₁ = 184,540 / ( 1+0.15) ^¹= 160,469.57

PV of CF₂ = 192,460 / ( 1+0.15)^² = 145,527.41

PV of CF₃ = 200,657 / ( 1+0.15)^³= 131,935.37

PV of CF₄ = 209,138 / ( 1+0.15)^⁴ = 119,575.52

PV of CF₅ = 242,910/ ( 1+0.15)^⁵ = 120,769.22

NPV = sum of all cash flows = -555000 + 160,469.57 + 145,527.41 + 131,935.37 + 119,575.52 + 120,769.22 = 2,507.86

All calculations in excel are below: