1. Project L costs $60,000, it
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 theproject’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 theproject’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 theproject’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 theproject’s payback?
5. Project L costs $30,000, its expected cash inflows are $8,000per year for 8 years, and its WACC is 10%. What is the project’sdiscounted payback?
Answer:
1. Computationof NPV
Computation of Present value of Cashinflows
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 – Initialoutlay
= $ 70885.23 -$ 60000
= $ 10885.23
Hence NPV is $ 10885.23
2) Computationof 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( Discountingfactor at 13% * Cashflow) | Disc @ 16% [ 1/ ( 1+r)^n] | Discounting factor | Discounted Cashflows( Discountingfactor at 16% * Cashflow) | Disc @ 17% [ 1/ ( 1+r)^n] | Discounting factor | Discounted Cashflows( Discountingfactor 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% and17%
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) Computationof 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 / InitialOutlay ) ^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) Computationof 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 recoverour investment amount.
Pay back period = Years before full recovery + Unrecoveredamount 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 flowduring the year
= 4+ ( $ 30000-$25358.9236) / $4967.3706
=4+ $ 4641.0764/ $ 4967.3706
=4+0.9343
=4.9343 Years
Hence Discounted payback period is 4.9343years
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