Question

Project L costs $50,000, its expected cash inflows are $9,000 per year for 12 years, and its WACC is 11%. What is the project's NPV?

Project L costs $45,000, its expected cash inflows are $11,000 per year for 8 years, and its WACC is 8%. What is the project's discounted payback?

Project L costs $54,892.28, its expected cash inflows are $11,000 per year for 10 years, and its WACC is 14%. What is the project's IRR?

Project L costs $75,000, its expected cash inflows are $8,000 per year for 8 years, and its WACC is 9%. What is the project's MIRR?

Project L costs $75,000, its expected cash inflows are $10,000 per year for 10 years, and its WACC is 9%. What is the project's payback?

Answer 1

1.

NPV = PV of cash inflows - Initial investment

       = $ 9,000 x PVIFA (11%, 12) - $ 50,000

       = $ 9,000 x [1 - (1+0.11)^-12/0.11] - $ 50,000

       = $ 9,000 x [1 - (1.11)^-12/0.11] - $ 50,000

       = $ 9,000 x [(0.28584082361372-1)/0.11] - $ 50,000

      = $ 9,000 x (0.71415917638628/0.11) - $ 50,000

       = $ 9,000 x 6.49235614896616 - $ 50,000

       = $ 58,431.2053406955 or $ 58,431.21

NPV of project L is $ 58,431.21

b.

Year	Cash Flow	Computation of Discounted Factor	Discounted Factor @ 8 % (F)	Discounted Cash Flow (C x F)	Discounted ‘CUM Cash Flow
0	-$45,000	1/ (1+0.08)0	1	-$45,000	-$45,000
1	11,000	1/ (1+0.08)1	0.9259259259	10,185.18519	-34,814.81481
2	11,000	1/ (1+0.08)2	0.8573388203	9,430.72702	-25,384.08779
3	11,000	1/ (1+0.08)3	0.7938322410	8,732.15465	-16,651.93314
4	11,000	1/ (1+0.08)4	0.7350298528	8,085.32838	-8,566.60476
5	11,000	1/ (1+0.08)5	0.6805831970	7,486.41516	-1,080.18959
6	11,000	1/ (1+0.08)6	0.6301696269	6,931.86589	5,851.67630
7	11,000	1/ (1+0.08)7	0.5834903953	6,418.39434	12,270.07065
8	11,000	1/ (1+0.08)8	0.5402688845	5,942.95773	18,213.02838

Discounted payback period = A + B/C

A = Last period number with a negative cumulative discounted cash flow = 5

B = Absolute value of cumulative discounted cash flow at the end of period A = $ 1,080.18959

C = Total discounted cash flow during the period following period A = $ 6,931.86589

Discounted payback period = 5 + $ 1,080.18959/$ 6,931.86589 = 5 + 0.155829557 = 5.16 years

Discounted payback period of project L is 5.16 years

3.

Computation of IRR using trial and error method:

Computation of NPV at discount rate of 15 %:

Year	Cash Flow (C)	Computation of PV Factor	PV Factor @ 15 % (F)	PV (C x F)
0	-$54,892.28	1/ (1+0.15)0	1	-$54,892.28
1	11,000	1/ (1+0.15)1	0.869565217	9,565.217391
2	11,000	1/ (1+0.15)2	0.756143667	8,317.580340
3	11,000	1/ (1+0.15)3	0.657516232	7,232.678557
4	11,000	1/ (1+0.15)4	0.571753246	6,289.285702
5	11,000	1/ (1+0.15)5	0.497176735	5,468.944088
6	11,000	1/ (1+0.15)6	0.432327596	4,755.603555
7	11,000	1/ (1+0.15)7	0.37593704	4,135.307439
8	11,000	1/ (1+0.15)8	0.326901774	3,595.919512
9	11,000	1/ (1+0.15)9	0.284262412	3,126.886532
10	11,000	1/ (1+0.15)10	0.247184706	2,719.031767
			NPV 1	$ 3,14.174884

As NPV is positive let’s compute NPV at discount rate of 16 %.

Year	Cash Flow (C)	Computation of PV Factor	PV Factor @ 16 % (F)	PV (C x F)
0	-$54,892.28	1/ (1+0.16)0	1	-$54,892.28
1	11,000	1/ (1+0.16)1	0.862068966	9,482.758621
2	11,000	1/ (1+0.16)2	0.743162901	8,174.791914
3	11,000	1/ (1+0.16)3	0.640657674	7,047.234409
4	11,000	1/ (1+0.16)4	0.552291098	6,075.202077
5	11,000	1/ (1+0.16)5	0.476113015	5,237.243170
6	11,000	1/ (1+0.16)6	0.410442255	4,514.864801
7	11,000	1/ (1+0.16)7	0.35382953	3,892.124828
8	11,000	1/ (1+0.16)8	0.305025457	3,355.280025
9	11,000	1/ (1+0.16)9	0.26295298	2,892.482780
10	11,000	1/ (1+0.16)10	0.226683603	2,493.519638
			NPV2	-$1,726.777737

IRR = R1 + [NPV1 x (R2 – R1)/ (NPV1 – NPV2)]

= 15 % + [$ 3,14.174884 x (16 % - 15 %)/ ($ 3,14.174884 – (-$1,726.777737))]

= 15 % + [($ 3,14.174884 x 1 %)/ ($ 3,14.174884 + $ 1,726.777737)]

= 15 % + ($ 3.14174884/ $ 2,040.952621)

= 15 % + 0.001539354

= 15 % + 0.15 % = 15.15 %

IRR of project L is 15.15 %

4.

Year	Cash Flow (C)	Computation of FV Factor	FV Factor @ 9 % (F)	FV (F x C)
1	$ 8,000	(1+0.09)8	1.828039121	$14,624.312967
2	$ 8,000	(1+0.09)7	1.677100111	13,416.800887
3	$ 8,000	(1+0.09)6	1.538623955	12,308.991639
4	$ 8,000	(1+0.09)5	1.41158161	11,292.652880
5	$ 8,000	(1+0.09)4	1.295029	10,360.232
6	$ 8,000	(1+0.09)3	1.1881	9,504.80
7	$ 8,000	(1+0.09)2	1.09	8,720.00
8	$ 8,000	(1+0.09)1	1	8,000.00
			Terminal Cash Flow	$ 88,227.790373

MIRR = ⁿ √ (Terminal cash flow/Outlay) – 1

          = ⁸ √ ($ 88,227.790373/$ 75,000) – 1

          = ($ 1.17637053830667) ^1/8 – 1

         = ($ 1.17637053830667) ^0.125 – 1

          = 1.02051176863969 – 1

          = 0.02051176863969 or 2.05 %

MIRR of project L is 2.05 %

5.

Payback period for even cash flows = Initial investment /Annual cash flow

= $ 75,000/$ 10,000 = 7.5 years

Payback period of project L is 7.5 years