Review ofDomesticCapitalBudgetingWe can use CF, = (OCF)(1 - t) + tDto restate the NPV equation,TCF,TVTZNPV =Co+(1 + K)T+ K)tt=1(1as:1(OCF)(1 - t) + DTVTZNPV =XCo(1 + K))(1 + K)t = 1
Review of Domestic Capital Budgeting We can use CFt = (OCFt )(1 – ) + Dt to restate the NPV equation, as: NPV = S t = 1 T CFt (1 + K) t – C0 TVT (1 + K) T + NPV = S t = 1 T (OCFt )(1 – ) + Dt (1 + K) t – C0 TVT (1 + K) T +
The Adjusted Present ValueModelTT(OCF)(1 -tDtTVTZ2NPV二C+(1 + K))+ K)t=(1(1 + K)t = 1can be converted to adjusted present value(APYbCF)(1 - t)tD,tI,TVTAPVC(1 + K,)7(1 +i)(1 +i)(1 + K)t = 1by appealing to Modigliani and Miller's results
The Adjusted Present Value Model can be converted to adjusted present value (APV) by appealing to Modigliani and Miller’s results. NPV = S t = 1 T (OCFt )(1 – ) (1 + K) t C0 TVT (1 + K) T + Dt (1 + K) t + S – t = 1 T APV =S t = 1 T (OCFt )(1 – ) (1 + Ku ) t C0 TVT (1 + Ku ) T + Dt (1 + i) t + – It (1 + i) t +
The AdjustedPresentValueModelT(OCF)(1- T)tD,tITVTAPV-Z(1 + K,)(1 + K)(1 + i)(1 + i)t =1&TheAPVmodelisavalueadditivityapproachtocapital budgeting. Each cash flow that is asource of value to the firm is consideredindividuallyNote that with the APV model, each cash flow isdiscounted at a rate that is appropriate to theriskiness of the cash flow
The Adjusted Present Value Model ❖The APV model is a value additivity approach to capital budgeting. Each cash flow that is a source of value to the firm is considered individually. ❖Note that with the APV model, each cash flow is discounted at a rate that is appropriate to the riskiness of the cash flow. APV =S t = 1 T (OCFt )(1 – ) (1 + Ku ) t C0 TVT (1 + Ku ) T + Dt (1 + i) t + – It (1 + i) t +
DomesticAPVExampleConsider a project where the timing and size of theincremental after-tax cash flows for an all-equity firm are$500-$1,000$125$250$37511K?120134CF=-$1000 The unlevered cost of equity is ro = 10%:The project would be rejected byCF1$125an all-equity firmCF2$2501= 10CF3$375NPV=-$56.50CF4二$500
Domestic APV Example Consider a project where the timing and size of the incremental after-tax cash flows for an all-equity firm are: 0 1 2 3 4 –$1,000 $125 $250 $375 $500 The unlevered cost of equity is r0 = 10%: The project would be rejected by an all-equity firm: CF0 = –$1000 CF1 = $125 CF2 = $250 CF3 = $375 I = 10 NPV = –$56.50 CF4 = $500
DomesticAPVExample(continued) Now, imagine that the firm finances theproject with $600 of debt at r = 8%. The tax rate is 40%, so each year they havean interest tax shield worth $19.20:T X / = .40 X ($600 X .08)= .40 X $48= $19.20
Domestic APV Example (continued) ❖Now, imagine that the firm finances the project with $600 of debt at r = 8%. ❖The tax rate is 40%, so each year they have an interest tax shield worth $19.20: × I = .40 × ($600 × .08) = .40 × $48 = $19.20