ALSALEH- Fin 421: Chapter 5 1 Part II Capital Investment Choice Chapter 5 Measuring Investment...

ALSALEH- Fin 421: Chapter 51

Part II Capital Investment Choice Chapter 5

Measuring Investment Value:You Can Trust NPV


Definition and Illustration of NPVAn investment’s net present value is the sum ofthe present values of its expected benefits,minus the present value of cash Outlays.

NPV = CF1 CF2 CFn

(1+k)1 (1+k)2 (1+k)n1++

The arbitrage pricing principal requires that the value of an investment is the sum of the present value of all future cash flows.

(5-1)


NPV Example: Y0 Y1 Y2($1500) $1,000 $1,000

At k =10 percent

NPV = ($1,000 x PVIFA12yr,10%) - $1,500 = $1,735.50 - $1,500 = $235.50


Complex Cash FlowsCash flows are typically not even over the life of a capital investment, and there may be outlays in more than one period.There is no requirement that all future

cash flows are positive Table 5-1- page141

$-1,000 1,000 -2,000 3,000

10%


PerpetuitiesThe NPV of a perpetuity with a constant cash flow is:

NPV = CF1 /(k - g) - I0 (5-2)

Example: $5.1 billion is paid for perpetual cash flows of $700 million at the end of each year. What is investment’s NPV at 15 percent required Return.NPV = $700/(.15 – 0) - $5,100 = -$433mNPV@ g=4%= $700/(.15-.04) -$5,100 = $1,264m


Forms of Computing NPV a. PV value of cash benefits, minus the present

value of cash costs other than financing costs, discounted at average cost of debt and equity funds

a. PV of cash flows to stockholders, discounted at the stockholders’ opportunity cost.

a. PV of economic profits, discounted at the stockholders’ opportunity cost


Net Present Value and Wealth CreationPerfect Financial Marketsa. All-Equity Financing

Cash flow from an investment is available to distribute to the stockholders or reinvest on their behalf.

The value of an investment opportunity is the same whether the equity portion of its funding came from retention of earnings or the sale of new stock.


Example- Table 5-2. Berner CorporationPage 144

Year 0 1 2CF (1,500.00) 1,200.00 800.00PV@12% (1,500.00) 1,071.43 637.75Total PV 1,709.18NPV = 209.18


b. Debt-Equity Mix and NPV

NPV measures wealth creation for shareholders when debt is included in the financing and maintained at a constant percentage of present value of future cash Flows.

When investment is financed with a combination of debt and equity, the average opportunity cost is referred to as the weighted average cost of capital (WACC).


WACC = Wd Kd + (1-Wd)Ke (5-3)

Wd = 50% of value of investment, Kd , Interestcreditors expect to earn on assets of similar

risk, Ke= return required by stockholders

If Kd = 10%, Ke = 14%, (taxes=0) then WACC= 0.5 x 0.10 + (1- 0.5) x 0.14 = 12%


Table 5-3YEAR 0 1 2

CF from investment (1,500.00) 1,200.00 800.00PV of remaining CF(12%) 1,709.18 714.29 0.00Debt (50% of PV of rem. CF) 854.59 357.14 0.00Borrow (repay) 854.59 (497.45) (357.14)

CF from investment (1,500.00) 1,200.00 800.00Interest expense 85.46 35.71Borrow (repay) 854.59 (497.45) (357.14)CF to (from) equity (645.41) 617.09 407.15PV (14%) (645.41) 541/30 313.29PV 845.59

NPV 209.18


Market Imperfection Income Taxes, NPV, and Wealth Creation With or without taxes, and with or without

debt, the net present value is the amount by which an investment increases the wealth of the shareholders.

Tax consideration1. Cost of capital asset is expensed over the

useful life of the asset (depreciation).2. Interest on debt is tax deductible


Example- Berner Corporation- Page 146-147

Purchase price of the asset = $1,500The asset has a useful life of 2 yearsFirst years depreciation = $900Second year depreciation = $600

Tax rate = 40 percentYear 1 tax : ($1,200 -$900) x 0.4 = $120Year 2 tax: ($800 -$600) x 0.4 = $80


Table 5-4 0 1 2

CF from investment (1,500.00) 1,200.00 800.00-Tax 120.00 80.00After tax flow from investmentAfter tax flow from investment Without interest expenseWithout interest expense (1,500.00) 1,080.00(1,500.00) 1,080.00 720.00 720.00PV of rem.CF at WACC of 10% 1,576.86 654.55 0.00Debt (50% of PV of rem. CF) 788.43 327.28 0.00Borrow (repay) 788.43 (461.15) (327.28)

After tax CF from investment (1,500.00) 1,080.00 720.00Interest expense ( 78.84) ( 32.73)Interest savings 31.54 13.09Borrow (repay) 788.43 (461.15) (327.28)CF to (from) equity (711.57) 571.55 373.08PV (14%) (711.57) 501.36 287.07PV 788.43NPV 76.86


Tax deductibility of interest

Interest before tax , Kd= 10%, K=14%e

Tax rate = 40 %Cost of debt after tax = 10%( 1-Tax rate)

= 10%(1-0.4) = 10% (0.6) = 6%

Savings = 4% =10%x 0.4Tax savings = (cost before tax) x Tax rateWACC = .06x 0.5 + .14 x.50 = 10%


Net present value of the investment (NPV)can be calculated by:

1. discounting future cash flows from investment at the cost of capital Minus 2. the cost of the investment

NPV = $1,080/(1.101) + $720/(1.102) - $1,500 = $76.86


NPV after tax cash flows from investment, after considering the impact of financing choice, discounted at the weighted average cost of capital

Wealth gain to the stockholders, based on an analysis of the cash flows to and from the stockholders, considering the stockholders’ opportunity cost.


Three Methods of Computing NPV a. PV value of cash benefits, minus the present

value of cash costs discounted at average cost of capital (Page 148).

b. PV of cash flows to stockholders, discounted at the stockholders’ opportunity cost ( Figure 5-4, page 147)

c. PV of economic profits, discounted at the stockholders’ opportunity cost (Figure 5-5- page 149)


Uninformed Investors and NPVRepresent a serious problem The market value of the stock may be different

from its intrinsic valueLead to the rejection of attractive investmentsHoweverInvestor’s mistaken view is temporaryInvestors become informed over time as cash

flows come in


The impact of a new investment onIntrinsic Value if the stockholders aremisinformed:

Given NPVi = the intrinsic value of a Proposed capital investment

NPVi = IEn ( So / Sn ) – IEo ---------------- 5-7


NPVi = intrinsic net present value of a proposed capital investment

IEn = intrinsic value of the equity with the proposed capital investmentIEo = intrinsic value of the equity without the proposed capital investmentSn = number of shares of stock if the new investment is madeSo = number of shares of stock outstanding


Example: Albers CorporationThe Corp. generates cash flow of $1million a yearThe company has 100,000 shares of stock Outstanding.Cash flow per share is $10The company’s cost of capital is 10 percentStockholders are misinformed and expect cash flow of only $8 a share


Per share T. EquityIntrinsic $10/0.10=$100 $100x100,000 =$10,000,000value Actual $ 8/0.10= $ 80 $ 80x100,000 = $80,000,000Price The company has an attractive investment opportunity that requires $2 million of additional equity PV of the cash inflows from investment is $2.4 $2 million of needed equity will be obtained by selling new shares = $2,000,000/ $8 = 25,000 shares Sn = 100,000 + 25,000 = 125,000 shares

NPVi = $12,400,000 (100,000/125,000) -$10,000,000 = ($80,000)


The best solution to the problem ofmisinformed investors:

Make extra efforts to make good estimates of future benefits. Communicate honestly with the investors to

keep them well informed about their company and its future investment opportunities.


NPV = (1,080 –D1 - 0.10 X 1500)/1.10 +[720 – (1,500 –D1 ) - 0.10 (1,500 –D1)]/(1.10)2

Rearranging termsNPV = (1,080 - 0.10 X 1500)/1.10 +(720 -1,500 - 0.10 X 1,500)/(1.10 )2

- D1 /1.10 +1.10 D1 /(1.10)2

NPV = (720 -1,500 - 0.10 X 1,500)/(1.10 )2

ALSALEH- Fin 421: Chapter 5 1 Part II Capital Investment Choice Chapter 5 Measuring Investment...

Documents

Transcript of ALSALEH- Fin 421: Chapter 5 1 Part II Capital Investment Choice Chapter 5 Measuring Investment...