Question

Davis Industries must choose between a gas-powered and an electric-powered forklift truck for moving materials in its factory. Because both forklifts perform the same function, the firm will choose only one. (They are mutually exclusive investments.) The electric-powered truck will cost more, but it will be less expensive to operate; it will cost $21,500, whereas the gas-powered truck will cost $17,960. The cost of capital that applies to both investments is 13%. The life for both types of truck is estimated to be 6 years, during which time the net cash flows for the electric-powered truck will be $6,860 per year, and those for the gas-powered truck will be $4,600 per year. Annual net cash flows include depreciation expenses. Calculate the NPV and IRR for each type of truck, and decide which to recommend.

Do not round intermediate calculations. Round the monetary values to the nearest dollar and percentage values to two decimal places.

Answer 1

Step 1 : Identification of Alternatives

Alternative 1 : Electric-powered forklift truck
Alternative 2 : Gas-powered forklift truck

Step 2 : Calculation of NPV & IRR

Net Present Value = Present Value of Cash Inflows - Present Value of Cash Outflows
IRR is the rate of return at which NPV = 0

(a) (i) Calculation of NPV in Alternative 1 - Electric-powered forklift truck
Given: Cost of Capital = 13%

Particulars	Period	Amount	PVF @ 13%	Present Value
Cash Outflows:
Cost of Truck	0	($21,500.00)	1	($21,500.00)
Cash Inflows:
Annual Net Cash flows	1-6	$6,860.00	3.997549789	$27,423.19
Net Present Value				$5,923.19

(a) (ii) Calculation of IRR in Alternative 1 Electric-powered forklift truck

IRR will be calculated using trial & error method.
At discount rate = 13%, NPV = $5,923.19. IRR ia the rate of Return at which NPV = 0. Therefore, we need to discount at a higher rate.

Let discount rate = 22%

Calculation of NPV at discount rate = 22%

Particulars	Period	Amount	PVF @ 22%	Present Value
Cash Outflows:
Cost of Truck	0	($21,500.00)	1	($21,500.00)
Cash Inflows:
Annual Net Cash flows	1-6	$6,860.00	3.166917837	$21,725.06
Net Present Value				$225.06

At discount rate = 22%, NPV = $225.06. Therefore we need to discount at a higher rate.

Let discount rate = 23%

Calculation of NPV at discount rate = 23%

Particulars	Period	Amount	PVF @ 23%	Present Value
Cash Outflows:
Cost of Truck	0	($21,500.00)	1	($21,500.00)
Cash Inflows:
Annual Net Cash flows	1-6	$6,860.00	3.092254453	$21,212.87
Net Present Value				($287.13)

At discount rate = 23%, NPV = ($287.13). Therefore, IRR lies between 22% & 23%

Using interpolation
IRR = 22% + $225.06 / $225.06-(-$287.13)
IRR = 22% + $225.06 / $512.19
IRR = 22% + 0.4393994
IRR = 22.44 % approx.

(b) (i) Calculation of NPV in Alternative 2 Gas-powered forklift truck.
Given Cost of Capital = 13%

Particulars	Period	Amount	PVF @ 13%	Present Value
Cash Outflows:
Cost of Truck	0	($17,960.00)	1	($17,960.00)
Cash Inflows:
Annual Net Cash flows	1-6	$4,600.00	3.997549789	$18,388.73
Net Present Value				$428.73

(b) (ii) Calculation of IRR in Alternative 1 Gas-powered forklift truck.

IRR will be calculated using trial & error method.
At discount rate = 13%, NPV = $428.73. IRR ia the rate of Return at which NPV = 0. Therefore we need to discount at a higher rate.

Let discount rate = 14%

Calculation of NPV at discount rate = 14%

Particulars	Period	Amount	PVF @ 13%	Present Value
Cash Outflows:
Cost of Truck	0	($17,960.00)	1	($17,960.00)
Cash Inflows:
Annual Net Cash flows	1-6	$4,600.00	3.888667517	$17,887.87
Net Present Value				($72.13)

At discount rate = 14%, NPV = ($72.13). Therefore, IRR lies between 13% & 14%

Using interpolation
IRR = 13% + $428.73 / $428.73-(-$72.13)
IRR = 13% + $428.73 / $500.86
IRR = 13% + 0.855988
IRR = 13.86 % approx.

Decision:

Alternatives	NPV	IRR
Electric-powered forklift truck	$5,923.19	22.43%
Gas-powered forklift truck	$428.73	13.85%

Select Electric-powered forklift truck as NPV & IRR of Electric-powered forklift truck is higher than that of Gas-powered forklift truck indicating more value addition.

Note :
PVF(r,t) = (1/(1+r))^n
PVAF = (1/(1+r))^1 + (1/(1+r))^2 +...+(1/(1+r))^n
or you can use Present value factor tables