npv analysis spreadsheet

Question 1:

Option 1 Purchase without Finance

Cost of Capital 10%

0 -11,400,000 0 0 -11,400,000 1.000 -11,400,0001 0 70,949 0 70,949 0.909 64,4992 0 80,300 0 80,300 0.826 66,3643 0 80,300 0 80,300 0.751 60,3314 0 80,300 0 80,300 0.683 54,8465 0 80,300 0 80,300 0.621 49,8606 0 80,300 0 80,300 0.564 45,3277 0 80,300 0 80,300 0.513 41,2078 0 80,300 0 80,300 0.467 37,4619 0 80,300 11,870,074 11,950,374 0.424 5,068,125

Total -11,400,000 713,349 -11,007,851 -5,911,981

NPV -5,911,981 5,488,019IRR 1.13%MCR (Max Capital at Risk) 11,400,000B/C (Benefit to Cost ratio) 0.481

Option 2 Purchase with FinanceCost of Capital 10%

0 -3,579,000 0 0 -3,579,000 1.000 -3,579,0001 0 -503,617 0 -503,617 0.909 -457,8342 0 -505,025 0 -505,025 0.826 -417,3763 0 -510,180 0 -510,180 0.751 -383,3064 0 -515,763 0 -515,763 0.683 -352,2735 0 -521,809 0 -521,809 0.621 -324,0026 0 -528,357 0 -528,357 0.564 -298,2447 0 -535,449 0 -535,449 0.513 -274,7708 0 -543,129 0 -543,129 0.467 -253,3749 0 -551,446 5,727,858 5,176,412 0.424 2,195,304

Total -£3,579,000 -£4,714,775 -£6,135,394 -£4,144,874

NPV -4,144,874 -565,874IRR -6.21%MCR (Max Capital at Risk) 6,340,178B/C (Benefit to Cost ratio) 0.346

Option 2 LeaseCost of Capital 10%

0 0 0 0 0 1.000 01 0 -660,000 0 -660,000 0.909 -600,0002 0 -660,000 0 -660,000 0.826 -545,455

Years Discounted

Capital Investment

Project's Cash Flows

(AT)Residual

valueNet Cash

flows (AT)Discount

factorPresent Value of Cash flows

Years Discounted

Capital Investment

Project's Cash Flows

(AT)Residual

valueNet Cash

flows (AT)Discount

factorPresent Value of Cash flows

Years Discounted

Capital Investment

Project's Cash Flows

(AT)Residual

valueNet Cash

flows (AT)Discount

factorPresent Value of Cash flows

3 0 -660,000 0 -660,000 0.751 -495,8684 0 -660,000 0 -660,000 0.683 -450,7895 0 -660,000 0 -660,000 0.621 -409,8086 0 -726,000 0 -726,000 0.564 -409,8087 0 -726,000 0 -726,000 0.513 -372,5538 0 -726,000 0 -726,000 0.467 -338,6849 0 -726,000 0 -726,000 0.424 -307,895

Total 0 -6,204,000 -3,300,000 -3,930,859

NPV -3,930,859

Amounts in $

-11,400,000-11,335,501-11,269,137-11,208,807-11,153,961-11,104,101-11,058,773-11,017,567-10,980,106

-5,911,981

Amounts in $

-3,579,000-4,036,834-4,454,210-4,837,515-5,189,789-5,513,791-5,812,035-6,086,805-6,340,178-4,144,874

Amounts in $

0-600,000

-1,145,455

Cum. discounted cash flow

Cum. discounted cash flow

Cum. discounted cash flow

-1,641,322-2,092,111-2,501,919-2,911,727-3,284,280-3,622,964-3,930,859

Present Value of Cash flowsPV = Cash Flow / (1 + r) ^ t

End of Year Lease Lease Purchase vs lease

1 -11400000 -3579000 0 0 -11,400,000 -3,579,000 0 -78210000

2 70,949 -503617 -660000 1 64,499 -457,834 -600,000 574566

3 80,300 -505025 -660000 2 66,364 -417,376 -545,455 585,325

4 80,300 -510180 -660000 3 60,331 -383,306 -495,868 590480

5 80,300 -515763 -660000 4 54,846 -352,273 -450,789 596063

6 80,300 -521809 -660000 5 49,860 -324,002 -409,808 602109

7 80,300 -528357 -726000 6 45,327 -298,244 -409,808 608657

8 80,300 -535449 -726000 7 41,207 -274,770 -372,553 615749

9 80,300 -543129 -726000 8 37,461 -253,374 -338,684 623429

10 80,300 -551446 -726000 9 34,055 -233,867 -307,895 63174600

Residual Value 11,870,074 5,727,858 9 5,034,070 2,429,171 0 6142216

NPV -5,911,981 -4,144,874 -3,930,859 irr

214,015

Purchase without Financing

Purchase with Financing

Years discounted

(t)Purchase without

FinancePurchase with

Financing

###

Purchase vs lease Cash Flows After Tax ($)

1 Minus 3 2 minus 3 1 vs 20 -11400000 -3579000 -78210001 730,949 156383 5745662 740,300 154975 5853253 740,300 149820 5904804 740,300 144237 5960635 740,300 138191 6021096 806,300 197643 6086577 806,300 190551 6157498 806,300 182871 6234299 12,676,374 5902412 6773962

IRR Differetial 7% 9% 6%

Discounted Years

IRR Purchase se with Finance Lease

0.0% 1,183,423 (2,565,917) (6,204,000)1.0% 131,874 (2,825,732) (5,898,602)2.0% (821,393) (3,055,486) (5,614,696)3.0% (1,686,431) (3,258,558) (5,350,454)4.0% (2,472,178) (3,437,931) (5,104,230)5.0% (3,186,592) (3,596,242) (4,874,533)6.0% (3,836,767) (3,735,827) (4,660,013)7.0% (4,429,032) (3,858,751) (4,459,446)8.0% (4,969,041) (3,966,847) (4,271,722)9.0% (5,461,849) (4,061,741) (4,095,832)

10.0% (5,911,981) (4,144,874) (3,930,859)11.0% (6,323,493) (4,217,530) (3,775,967)12.0% (6,700,023) (4,280,849) (3,630,394)13.0% (7,044,836) (4,335,844) (3,493,444)14.0% (7,360,867) (4,383,420) (3,364,483)15.0% (7,650,757) (4,424,380) (3,242,928)16.0% (7,916,884) (4,459,443) (3,128,247)

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17%

-$10,000,000

-$8,000,000

-$6,000,000

-$4,000,000

-$2,000,000

$0

$2,000,000

Discount Rate Sensitivity

Purchase

Purchase with Finance

Lease

Discount Rate

NP

V

Option (1) IRR Firms opportunity Cost

a b c

Option 1: PV of Purchase without Finance

0 Initial Capital Investment + PV of Purchase without Finance

1 Relevant Benefits (Rental Savings)

9 Relevant Benefits (Rental Savings) + Residual Value

Years from Project Launch

PV of Purchase without Finance

Option 1 Option 2

NPV $ -5,911,981 $ -4,144,874

0.519 -0.8419

Purchase without Finance

Purchase with Finance

Option 3

Lease

$ -3,930,859

profitability index = npv of cash inflows /

iinitial invesment

Option 1 Purchase without Finance

Discount rate 10%

Discounted year 0 1 2 3 4 Capital Investment -11,400,000Relavent Savings 70,949 80,300 80,300 80,300Residual valueCash flows -11,400,000 70,949 80,300 80,300 80,300

Discount factor 1.000 0.909 0.826 0.751 0.683 Discounted cash flow -11,400,000 64,499 66,364 60,331 54,846Cum. discounted cash flow -11,400,000 -11,335,501 -11,269,137 -11,208,807 -11,153,961

NPV -5,911,981IRR 1.13%MCR (Max Capital at Risk) 11,400,000B/C (Benefit to Cost ratio) 0.481

Option 2 Purchase with Finance

Discount rate 10%

Discounted year 0 1 2 3 4 Income 0 -503,617 -505,025 -510,180 -515,763Capital -3579000 0 0 0 0Cash flow -3,579,000 -503,617 -505,025 -510,180 -515,763

Discount factor 1.0000 0.9091 0.8264 0.7513 0.6830Discounted cash flow -3,579,000 -457,834 -417,376 -383,306 -352,273Cum. discounted cash flow -3,579,000 -4,036,834 -4,454,210 -4,837,515 -5,189,789

NPV -4,144,874IRR -6.21%MCR (Max Capital at Risk) 6,340,178B/C (Benefit to Cost ratio) 0.346

Option 3 Lease

Discount rate 10%

Discounted year 0 1 2 3 4 Income 0 -660,000 -660,000 -660,000 -660,000Capital 0 0 0 0Cash flow 0 -660,000 -660,000 -660,000 -660,000

Discount factor 1 1 1 1 1Discounted cash flow 0 -600,000 -545,455 -495,868 -450,789Cum. discounted cash flow 0 -600,000 -1,145,455 -1,641,322 -2,092,111

NPV -3,930,859IRR Err:523MCR (Max Capital at Risk) 3,930,859B/C (Benefit to Cost ratio) 0.000

5 6 7 8 9 Total-11,400,000

80,300 80,300 80,300 80,300 80,300 713,349

11,870,07480,300 80,300 80,300 80,300 11,950,374 -11,007,851

0.621 0.564 0.513 0.467 0.424 49,860 45,327 41,207 37,461 5,068,125 -5,911,981

-11,104,101 -11,058,773 -11,017,567 -10,980,106 -5,911,981

5 6 7 8 9 Total

-521,809 -528,357 -535,449 -543,129 -551,446 -4,714,7750 0 0 5,727,858 2,148,858

-521,809 -528,357 -535,449 -543,129 5,176,412 -2,565,917

0.6209 0.5645 0.5132 0.4665 0.4241-324,002 -298,244 -274,770 -253,374 2,195,304 -5,513,791

-5,513,791 -5,812,035 -6,086,805 -6,340,178 -4,144,874

-503617-505025-510180-515763-521809-528357-535449-543129-551446

5 6 7 8 9 Total

-660,000 -726,000 -726,000 -726,000 -726,000 -6,204,0000 0 0 0 5,727,858

-660,000 -726,000 -726,000 -726,000 -726,000 -6,204,000

1 1 1 0 0-409,808 -409,808 -372,553 -338,684 -307,895 -3,930,859

-2,501,919 -2,911,727 -3,284,280 -3,622,964 -3,930,859