Question

1. Project L costs $60,000, its expected cash inflows are $13,000 per year for 11 years, and its WACC is 14%. What is the project's NPV?

2. Project L costs $46,352.00, its expected cash inflows are $11,000 per year for 8 years, and its WACC is 13%. What is the project's IRR?

3. Project L costs $75,000, its expected cash inflows are $14,000 per year for 8 years, and its WACC is 14%. What is the project's MIRR?

4. Project L costs $75,000, its expected cash inflows are $11,000 per year for 12 years, and its WACC is 14%. What is the project's payback?

5. Project L costs $30,000, its expected cash inflows are $8,000 per year for 8 years, and its WACC is 10%. What is the project's discounted payback?

Answer 1

1. Computation of NPV

Computation of Present value of Cash inflows

Cash inflows = $ 13000 per year

Time period = 11 years

WACC = 14%

We know that Present value of Ordinary Annuity = C * [ {1-( 1+i) ^-n} /i]

Here C = Cash flow per period

i = Rate of interest

n = No. of years

Present value of Cashflows accruing from Year 1 to 11 = $ 13000 [ { 1-( 1.14)^-11}/0.14]

= $ 13000[ { ( 1-0.2366} /0.14]

= $ 13000[ 0.76338/0.14]

= $ 13000*5.45271

= $ 70885.23

We know that NPV = Present value of future cash flows - Initial outlay

= $ 70885.23 -$ 60000

= $ 10885.23

Hence NPV is $ 10885.23

2) Computation of IRR

We know that at IRR, NPVshould be 0

Let us findout IRR by using Trial and error method

Year	Cash flow	Disc @ 13% [ 1/ ( 1+r)^n]	Discounting factor	Discounted Cashflows( Discounting factor at 13% * Cashflow)	Disc @ 16% [ 1/ ( 1+r)^n]	Discounting factor	Discounted Cashflows( Discounting factor at 16% * Cashflow)	Disc @ 17% [ 1/ ( 1+r)^n]	Discounting factor	Discounted Cashflows( Discounting factor at 17% * Cashflow)
0	($46,352)	1/( 1.13)^0	1	($46,352.0000)	1/( 1.16)^0	1	($46,352.0000)	1/( 1.17)^0	1.00000	($46,352.0000)
1	$11,000	1/( 1.13)^1	0.88496	$9,734.5133	1/( 1.16)^1	0.86207	$9,482.7586	1/( 1.17)^1	0.85470	$9,401.7094
2	$11,000	1/( 1.13)^2	0.78315	$8,614.6135	1/( 1.16)^2	0.74316	$8,174.7919	1/( 1.17)^2	0.73051	$8,035.6491
3	$11,000	1/( 1.13)^3	0.69305	$7,623.5518	1/( 1.16)^3	0.64066	$7,047.2344	1/( 1.17)^3	0.62437	$6,868.0761
4	$11,000	1/( 1.13)^4	0.61332	$6,746.5060	1/( 1.16)^4	0.55229	$6,075.2021	1/( 1.17)^4	0.53365	$5,870.1505
5	$11,000	1/( 1.13)^5	0.54276	$5,970.3593	1/( 1.16)^5	0.47611	$5,237.2432	1/( 1.17)^5	0.45611	$5,017.2227
6	$11,000	1/( 1.13)^6	0.48032	$5,283.5038	1/( 1.16)^6	0.41044	$4,514.8648	1/( 1.17)^6	0.38984	$4,288.2245
7	$11,000	1/( 1.13)^7	0.42506	$4,675.6671	1/( 1.16)^7	0.35383	$3,892.1248	1/( 1.17)^7	0.33320	$3,665.1492
8	$11,000	1/( 1.13)^8	0.37616	$4,137.7585	1/( 1.16)^8	0.30503	$3,355.2800	1/( 1.17)^8	0.28478	$3,132.6061
				$6,434.4732			$1,427.4998			($73.2124)

From the Above table we can say that IRR lies between 16% and 17%

By using interpolation technique we can find the exact IRR.

L.R +[ { NPV at L.R * ( H.R - L.R)}/ ( NPV at L.R - NPV at H.R) ]

Here L.R = Lower rate and H.R = Higher rate

=16% + [ { $ 1427.4998 ( 17% -16% ) } / [$ 1427.4998 -( -$73.2124)]

=16% + [ ( $ 1427.4998/ $ 1500.7123]

=16% +0.9512%

=16.9512%

Hence the IRR is 16.95%

3) Computation of MIRR

Given Cash flow per year = $ 14000

Reinvestment rate = 14%

Time Period = 8 Years

Computation of Terminal Cash flows

We know that Future Value of Ordimary Annuity = C [ { ( 1+i) ^n -1 ) /i]

Here C = Cash flow per period

I = Rate of interest

n = No.of Years

Future value of Cash flows = $ 14000[ { ( 1.14)^8-1} /0.14]

= $ 14000 [ { 2.85259-1} /0.14]

= $ 14000 { 1.85259/0.14]

= $ 14000*13.2328

=$ 185259.20

Hence the Terminal Cashflows is $ 185259.20

We know that MIRR = [  (Terminal Cash flow / Initial Outlay ) ^1/n -1]

= [ ($ 185259.20/ $ 75000)^ 1/8 -1]

= ( 2.47012 ) ^0.125 -1

= 1.11967-1

= 0.11967

Hence MIRR is 11.967%

4) Computation of Payback period

Year	Cashinflow	Cummulative cashinflows
1	$11,000	$11,000
2	$11,000	$ 11000+$ 11000= $ 22000
3	$11,000	$ 2200+$ 11000= $ 33000
4	$11,000	$ 33000+$ 11000= $ 44000
5	$11,000	$ 44000+$ 11000= $ 55000
6	$11,000	$ 55000+$ 11000= $ 66000
7	$11,000	$ 66000+$ 11000= $ 77000
8	$11,000	$ 77000+$ 11000= $ 88000
9	$11,000	$ 88000+$ 11000= $ 99000
10	$11,000	$ 99000+$ 11000= $ 110000
11	$11,000	$ 110000+$ 11000= $ 121000
12	$11,000	$ 121000+$ 11000= $ 132000

Pay Back period is nothing but within What time we can recover our investment amount.

Pay back period = Years before full recovery + Unrecovered amount at the start of the year / Cash flow during the year

= 6+ ( $ 75000-$ 66000) / $ 11000

= 6+ $ 9000/$ 11000

= 6+0.8182

= 6.8182

Hence Pay back period is 6.8182 Years

5) Compountation of Discounted pay back period

Year	Cashinflow	Disc @10% [ 1/(1+r)^n]	Discounting factor	Discounted cashflows( Cashinflow* Discounting factor)	Cummulative Cashinfows
1	$8,000	1/( 1.10)^1	0.9091	$7,272.7273	$7,272.73
2	$8,000	1/( 1.10)^2	0.8264	$6,611.5702	$7272.7273+$ 6611.5702= $ 13884.2975
3	$8,000	1/( 1.10)^3	0.7513	$6,010.5184	$ 13884.2975+$ 6010.5184 = $ 19894.8159
4	$8,000	1/( 1.10)^4	0.6830	$5,464.1076	$19894.8159+$ 5464.1076=$ 25358.9236
5	$8,000	1/( 1.10)^5	0.6209	$4,967.3706	$25358.9236+$ 4967.3706=$ 30326.2942
6	$8,000	1/( 1.10)^6	0.5645	$4,515.7914	$30326.2942+$ 4515.7914=$ 34842.0856
7	$8,000	1/( 1.10)^7	0.5132	$4,105.2649	$34842.0856+$ 4105.2649= $ 38947.3505
8	$8,000	1/( 1.10)^8	0.4665	$3,732.0590	3$8947.3505+$ 3732.0590=$ 42679.4096

Discounted Pay back period = Years before full recovery + Unrecovered amount at the start of the year /Discounted Cash flow during the year

= 4+ ( $ 30000-$25358.9236) / $4967.3706

=4+ $ 4641.0764/ $ 4967.3706

=4+0.9343

=4.9343 Years

Hence Discounted payback period is 4.9343 years

If you are having any doubts,plesae post a comment.

Thank you. Please rate it.