# 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?

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

If you are having any doubts,plesae post acomment.

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