Capital Budgeting. Capital Budgeting. Temporary assumption

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1 1 Capital Budgeting The I in Vfirm = f ( I, F, D) Capital Budgeting Process of deciding which long-term investments to make Current outlay followed by cash inflows beyond one year in the future New equipment, plants, new products Often replacing old equipment with new Expected return = required return? Temporary assumption Required return is given and is the same for all projects k = required return or the hurdle rate Assumption will be relaxed in the next chapter when we consider risk

2 5 steps to capital budgeting 1. Generation of investment proposals. Estimation of expected cash flows 3. Evaluation of expected cash flows 4. Selection of proposals 5. Continual reevaluation of proposals after acceptance We are mainly concerned with, 3 and 4 Estimation of expected cash flows Incremental CF of the firm with proposal vs. CF of firm without proposal After-tax what actually affects the common stockholders (available for retention or payout) CF = Net Income + Depreciation Incremental cash flows CF = ( S C D)(1 t) + D?S= change in sales revenue?c= change in operating costs?d= change in depreciation t = firm's marginal tax rate

3 Horizontal income statement Given : ( S C D) = (before - tax profits) if ( S C D)( t) = taxes then ( S C D)(1 t) = (after - tax profits) CF = ( S C D)(1 t) + D Replacement example Old equipment: original cost= 6, SV = 15 yr original life currently 5 yrs old with a MV = 8, New equipment: Cost = 4, SV = 4, 1 yr life S = +4,/yr C = -8,/yr NWC = 1, t = 5% k = 1% straight-line depr. on both Initial Outlay Purchase price new -Net proceeds sale of old + NWC $4, -4, +1, Initial Outlay $6, 3

4 4 Net proceeds from sale of old Net proceeds = MV t(mv BV) MV = market value, BV = book value D old = (Cost SV)/n = (6-)/15 = 4/yr BV = 6 5(4) = 4 Net proceeds = 8-.5(8-4) Net proceeds = 4 Net proceeds from sale of old Net proceeds = MV t(mv BV) What if MV>BV and machine is sold for a gain? Then there is a tax on the gain equal to t(mv-bv), and this tax is subtracted from the selling price to yield the net proceeds The formula works for gains or losses NWC NWC = current assets current liabilities NWC is additional motor oil or nuts and bolts needed to service the equipment NWC is additional cash that must be kept on hand if the proposal is accepted NWC is part of the initial outlay and is also a cash inflow at the end of the life of the project

5 5 Incremental Cash Flows ( CF) CF = ( S C D)(1 t ) + D S = 4/yr and C = -8/yr D old = 4 D new = (4-4)/1=36 D = 36 4 = -4/yr CF = [4 (-8) (-4)](1.5) - 4 CF = 58/yr for 1 years Terminal cash flow Often there is an extra cash inflow in the terminal year Return of the NWC = 1 since the motor oil, nuts and bolts, and cash are no longer needed Incremental salvage value SV = SV new SV old SV = 4 Total non-operating CF = = 14 Cash flow time line // Accept or reject? Isforecastedrateof return k = 1%? Lookslikea jobfor timevalue of money

6 6 Acceptance criteria Two discounted cash flow methods Internal Rate of Return (IRR) Net Present Value (NPV) Internal Rate of Return (IRR) IRR that discount rate that equates the present value of the expected cash inflows with the present value of the expected cash outflows IRR that discount rate that makes PV in = PV out Accept if IRR>=k and reject if IRR< k Internal Rate of Return (IRR) n CF1 CF CFn CFt CF = + + L+ = 1 n (1+ r) (1+ r) (1+ r) t = 1 (1+ r) CF = cash flow,end of period t t n = life of theproject r = IRR t

7 7 Internal Rate of Return = + + L+ 1 1 (1+ r ) (1+ r) (1+ r) Solve for r Accept if r = k Reject if r<k Finding IRR using a financial calculator: -6 CF j 58 CF j 9 N j 198 CF j IRR=.58% Slate of possible projects Project B C A D Outlay 1,,,, 5, 5, IRR 3% % 13% 7% % IRR Schedule B C A D IRR k Capital Raised Cumulative outlay

8 8 Net Present Value (NPV) NPV present value of the expected cash inflows minus the present value of the expected cash outflows when all cash flows are discounted at the required rate k Accept if NPV = Reject if NPV< n CF1 CF CFn CFt NPV = CF L + n = t (1+ k ) (1+ k ) (1 + k ) (1+ k ) CFt = cash flow, end of period t n = life of the project k = required rate of return Net Present Value (NPV) t= NPV = L+ 1 1 (1.1) (1.1) (1.1) Solve for NPV Accept if NPV = Reject if NPV< Finding NPV using a financial calculator: -6 CF j 58 CF j 9 N j 198 CF j I/YR 1 NPV=15,36.1

9 9 Another definition of IRR Since NPV = PV in - PV out and IRR makes PV in = Pv out IRR can be defined as the discount rate that makes NPV = k Quick summary Two alternative methods: NPV = PV inflows PV outflows discount at rate k IRR: PV inflows = PV outflows solve for IRR Accept if NPV = or IRR = k Reject if NPV< or IRR<k Quick summary of example NPV= L+ 1 1 (1.1) (1.1) (1.1) NPV= 15, = + 1 (1 + IRR) (1 + IRR) IRR =.58% L+ 1 (1+ IRR)

10 1 Single project: Same result Why IRR = k or NPV =? Pretend entire $6, outlay is financed by a 1 yr loan at interest rate = 1% Annual uniform payment to retire loan: 6 = R(PVIF a -1%-1) R=$431/yr Annual CF=58 plus extra 14 in yr 1 (58-431)(PVIF a -1%-1) + 14/(1.1) 1 = 1536 Possible conflict Period NPV(k =1%) IRR Project A % Project B %

11 11 Assumed reinvestment rates IRR All CF s reinvested at the IRR NPV All CF s reinvested at k NPV: more realistic, more conservative, more consistent Normally choose project with higher NPV Modified IRR (MIRR) Eliminates flaw of regular IRR method Assumes all CF s reinvested at k Compute sum of CF s at terminal point assuming reinvestment at k Solve for MIRR: discount rate that equates the PV of this terminal sum with initial outlay Modified IRR (MIRR) FV A,4 = 1(FVIFa-1%-4) = 46, = 4641 / (1 + MIRR A ) 4 MIRR A =18.4% FV B,4 = 5(1.1) +1(1.1) FV B,4 = 49, = 4975 / (1 + MIRR B ) 4 MIRR B =.5% Choose project B