Question

Machine A: This project costs $10 million. The expected net cash flows are $4 million per year for 4 years, when is to be replaced. Machine B: It costs $15 million, and has expected cash flows of $3.5 per year for 8 years, when it will be replaced. The cost of capital is 10%. Machine prices are expected to stay steady as production efficiencies are expected to offset inflation. Evaluate these projects. a. Calculate NPV, IRR, Replacement Chain, and Equivalent Annual Annuity. b. Which project should be company accept?

Answer 1

NPV = PV of Cash Inflows - PV of Cash Outflows

Machine A:

Year	CF (in M)	PVF @10%	Disc CF
0	$ -10.00	1.0000	$ -10.00
1	$      4.00	0.9091	$      3.64
2	$      4.00	0.8264	$      3.31
3	$      4.00	0.7513	$      3.01
4	$      4.00	0.6830	$      2.73
NPV			$      2.68

Machine B:

Year	CF (in M)	PVF @10%	Disc CF
0	$ -15.00	1.0000	$ -15.00
1	$      3.50	0.9091	$      3.18
2	$      3.50	0.8264	$      2.89
3	$      3.50	0.7513	$      2.63
4	$      3.50	0.6830	$      2.39
5	$      3.50	0.6209	$      2.17
6	$      3.50	0.5645	$      1.98
7	$      3.50	0.5132	$      1.80
8	$      3.50	0.4665	$      1.63
NPV			$      3.67

IRR is the Rate at which PV of Cash Inflows are equal to PV of Cash Outflows.

Machine A:

Year	CF	PVF @21%	Disc CF	PVF @22%	Disc CF
0	$ -10.00	1.0000	$ -10.00	1.0000	$ -10.00
1	$      4.00	0.8264	$      3.31	0.8197	$      3.28
2	$      4.00	0.6830	$      2.73	0.6719	$      2.69
3	$      4.00	0.5645	$      2.26	0.5507	$      2.20
4	$      4.00	0.4665	$      1.87	0.4514	$      1.81
NPV			$      0.16		$    -0.03

IRR = Rate at which least +ve NPV + [ NPV at that rate / change in NPV due to 1% inc in disc rate ] * 1%

= 21% + [ 0.16 / 0.19 ] * 1%

= 21% + 0.86%

= 21.86%

Machine B:

Year	CF	PVF @16%	Disc CF	PVF @17%	Disc CF
0	$ -15.00	1.0000	$ -15.00	1.0000	$ -15.00
1	$      3.50	0.8621	$      3.02	0.8547	$      2.99
2	$      3.50	0.7432	$      2.60	0.7305	$      2.56
3	$      3.50	0.6407	$      2.24	0.6244	$      2.19
4	$      3.50	0.5523	$      1.93	0.5337	$      1.87
5	$      3.50	0.4761	$      1.67	0.4561	$      1.60
6	$      3.50	0.4104	$      1.44	0.3898	$      1.36
7	$      3.50	0.3538	$      1.24	0.3332	$      1.17
8	$      3.50	0.3050	$      1.07	0.2848	$      1.00
NPV			$      0.20		$    -0.27

IRR = Rate at which least +ve NPV + [ NPV at that rate / change in NPV due to 1% inc in disc rate ] * 1%

= 16 % + [ 0.20 / 0.48 ] * 1%

= 16% + 0.42%

= 16.42%

Equivalent Annual Annuity:

NPV / PVAF(r%,n)

Machine A:

Equivalent Annuity = NPV / PVAF (r%,n)

= $ 2.68 / PVAF (10%, 4)

= $ 2.68 / 3.1699

= $ 0.8455 M

Machine B:

Equivalent Annuity = NPV / PVAF (r%,n)

= $ 3.67 / PVAF (10%, 8)

= $ 3.67 / 5.3349

= $ 0.6879 M

Part B:

Machine A is selected as Equivalent Annuity CF is more .