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課程 6:Refinancing* 再看一個資本預算的例題*再訪 Buy or Lease*Refinancing*How do we adjust discount rates to reflect risk?

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An example- IM&C projectIM&C - initial projections

0 1 2 3 4 5 6 71. Capital Investment 10,000 -10002. Accumulated depreciation 1,583 3167 4750 6333 7917 9500 03.Year-end book value 10,000 8,417 6,833 5,250 3,667 2,083 500 04.Working capital 500 1065 2450 3340 2225 1130 05.Total book value 10000 8917 7898 7700 7007 4308 1630 0 (3)+(4)6.Sales 475 10650 24500 33400 22250 111307.Cost of goods sold 761 6388 14690 20043 13345 66788.Other costs 4000 2000 1000 1000 1000 1000 10009,Depreciation 1,583 1,583 1,583 1,583 1,583 1,58310.Pretax profit -4,000 -3,869 1,679 7,227 10,774 6,322 1,869 500 (6)-(7)-(8)-(9)11.Tax at 35% -1400 -1354.15 587.65 2529.45 3770.9 2212.7 654.15 17512.Profit after tax -2,600 -2,515 1,091 4,698 7,003 4,109 1,215 325

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IM&C - revised projections reflecting inflation

0 1 2 3 4 5 6 71. Capital Investment 10,000 -19492. Accumulated depreciation 1,583 3167 4750 6333 7917 9500 03.Year-end book value 10,000 8,417 6,833 5,250 3,667 2,083 500 04.Working capital 550 1289 3261 4890 3583 2002 05.Total book value 10000 8967 8122 8511 8557 5666 2502 0 (3)+(4)6.Sales 523 12887 32610 48901 35834 197177.Cost of goods sold 837 7729 19552 29345 21492 118308.Other costs 4000 2200 1210 1331 1464 1611 17729,Depreciation 1,583 1,583 1,583 1,583 1,583 1,58310.Pretax profit -4,000 -4,097 2,365 10,144 16,509 11,148 4,532 1949 (6)-(7)-(8)-(9)11.Tax at 35% -1400 -1433.95 827.75 3550.4 5778.15 3901.8 1586.2 50712.Profit after tax -2,600 -2,663 1,537 6,594 10,731 7,246 2,946 942

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IM&C - cash flow analysis

0 1 2 3 4 5 6 71.Sales 523 12887 32610 48901 35834 197172.Cost of goods sold 837 7729 19552 29345 21492 118303.Other costs 4000 2200 1210 1331 1464 1611 17724.Tax at 35% -1400 -1433.95 827.75 3550.4 5778.15 3901.8 1586.25.Cash flow from operation -2,600 -1,080 3,120 8,177 12,314 8,829 4,529

6. Change in working capital -550 -739 -1972 -1629 1307 1581 20027.Capital investment -10,000 1,4428.Net cash flow -12,600 -1,630 2,381 6,205 10,685 10,136 6,110 3,4449.NPV at 20% 3519

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Buy or lease

• Steps:

1. Calculate the after-tax cash flows if the asset is leased and if it is purchased.

2. Calculate the present value of the after-tax cash outflows if leased and if purchased.

3. Compare the present value of the cost of leasing with the present value of the cost of borrowing to purchase.

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Example:

• Podunk Corporation needs a new machine priced at $100,000 that has an expected life of 6 years. The firm may either lease the asset or borrow to purchase it. The firm's marginal tax rate is 34%. Podunk plans to discount all cash flows, including the asset's salvage value, at the after tax cost of borrowing because all of the cash flows are considered to be low risk. With both alternatives, Podunk bears all maintenance, insurance, and other related costs, which are expected to be $2,000 per year.

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• Lease:

If the machine is leased, the annual lease payments will be six equal payments of $20,000 paid in advance. The lease contract does not require the lessee to purchase the machine at the end of the lease term.

• Purchase:

If the machine is purchased, the firm plans to use ACRS rates for 5-year property. The machine is expected to be sold for its estimated salvage value of $5,000 at the end of six years. Podunk can finance the purchase with a 12% term loan requiring six equal end-of-year payments consisting of principal and interest.

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Cash Flows: Leasing Alternative:End ofYear

LeasePaymen

t

Tax Savings[.34*(2)]

After-Tax Cash Outflowif Leased[(2) - (3)]

PresentValue @

8%

Present Value Cost ofLeasing [(4) x(5)]

(1) (2) (3) (4) (5) (6)

0 20,000 0 20,000 1.000 20,000

1 20,000 6,800 13,200 .926 12,223

2 20,000 6,800 13,200 .857 11,312

3 20,000 6,800 13,200 .794 10,481

4 20,000 6,800 13,200 .735 9,702

5 20,000 6,800 13,200 .681 8,989

6,800 (6,800) .630 (4,284)

$68,423

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Loan Amortization

End ofYear

BeginningBalance

LoanPayment

InterestPayment

PrincipalReduction

RemainingBalance

(1) (2) (3) (4) (5) (6)

1 100,000 24,325 12,000 12,325 87,675

2 87,675 24,325 10,521 13,804 73,871

3 73,871 24,325 8,865 15,460 58,411

4 58,411 24,325 7,009 17,316 41,095

5 41,095 24,325 4,931 19,394 21,701

6 21,701 24,325 2,604 21,721 0

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Present Value of After Tax Outflows (Purchased):

End ofYear

LoanPayment

InterestPayment

ACRSDepreciation

Tax DeductibleExpenses

[(3) + (4)]

TaxSavings

[.34 x(5)]

(1) (2) (3) (4) (5) (6)

1 24,325 12,000 20,000 32,000 10,880

2 24,325 10,521 32,000 42,521 14,457

3 24,325 8,865 19,200 28,065 9,542

4 24,325 7,009 11,520 18,529 6,300

5 24,325 4,931 11,520 16,451 5,593

6 24,325 2,604 5,760 8,364 2,844

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End ofYear

After Tax SalvageValue [S(1-.34)]

After Tax Cash

Outflow if Owned[(2)-(6)-(7)]

PresentValue at 8%

Present Value Cost ofOwning [(8)-(9)]

(7) (8) (9) (10)

1 0 13,445 .926 12,450

2 0 9,868 .857 8,457

3 0 14,783 .794 11,738

4 0 18,025 .735 13,248

5 0 18,732 .681 12,756

6 3,300 18,181 .630 11,454

$70,103

Present value cost of owning $70,103

Less present value cost of leasing 68,423

Advantage of leasing over owning $1,680

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Potential Advantages to Leasing:

Flexibility Financing Convenience

• Liquidity

• Shifts of risk of obsolescence

• Effective depreciation of land

• Tax considerations

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Potential Disadvantages to Leasing:

• Cost

• Lack of salvage value

• Difficulty of property improvements

• Noncancelability

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Mortgage Refinancing Decision• Falling interest rates create opportunities for refinancing

because the option is now “in the money”.• “Out of the money” mortgage may be refinanced for

other reasons.• Refinancing even in the case of falling rates may or may

not be beneficial.• To make a sound refinancing decision we must consider

the benefit as well as the cost of refinancing.

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Variables Influencing Refinancing Decision

• Cf.: Existing loan versus new loan

1.Mortgage type

2.Interest rate

3.Mortgage maturity

4.Prepayment penalty

5.Financing costs

6.Holding period

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An illustration: The Original loan

AssumptionsExisting Mortgage·Original loan amount $50,000

·Interest Rate 12 percent

·Term 30 years

·Age of mortgage 5 years

·Prepayment Penalty 5 percent

. Monthly payment

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Parameters of new loanNEW MORTGAGE

·Loan Amount = Outstanding balance on old loan

·Interest rate = 10½ percent

·Term = 25 years

·Refinancing costs = 3%

·Holding period = Hold mortgage until maturity

·Borrower's = 13 percent

opportunity rate

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Refinancing Decision

Determine Outstanding Balance on Old Loan

First determine monthly payment

$50,000 = PV

12/12 = i

30 x 12 = n

PMT = $514.30This is the monthly payment on the existing mortgage.

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Refinancing Decision

Outstanding balance at the end of 5th year

$514.30 = PMT

12/12 = i

25 x 12 = n

PV = $48,831

Therefore the outstanding balance on the old loan

= $48,831

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Refinancing Decision

Determine Monthly Payment on New Loan Payment:

$48,831 = PV

10.5/12 = i

25 x 12 = n

PMT = $461.05

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Refinancing Decision

Determine Cost of Refinancing

Prepayment Penalty on existing loan

= .05 x $48,831

=$2,442

Plus financing cost on new loan

= .03 x $48,831

= $1,465

TOTAL : $3,907

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Refinancing Decision

Determine Benefit of Refinancing

Monthly payments on existing loan = $514.30

Less Monthly payments on new loan= 461.05

$53.25This means that we are investing $3,907 today in order to save $53.25

every month for the next 25 years.

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Refinancing Decisions

Determine Present Value of Savings

Present value of savings

$53.25 = PMT

13 /12 = i

25 x 12 = n

PV = $4,721Net present value=$4,721-3,907=$814.

The refinancing is worth undertaking under our assumption.

What is the yield on this mortgage refinancing investment?

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Question:Shorter holding period

• What happens if we assume the borrower’s holding period is only 10 years?– 1.The cost of refinancing, $3,907, will be the

same.– 2.The benefit of refinancing will change.

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Determine Benefit of Refinancing

• 1. Monthly savings on mortgage payment

Monthly payments on existing loan = $514.30

Less Monthly payments on new loan= 461.05

$53.25

This amount is equal to that under the first example, but we will receive this saving for only 120 months and not 300 months as was the case in the first example.

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2. Lump sum saving• Determine the outstanding balance on old loan at the end of 15

years.

$514.30 = PMT

12/12 = i

15 x 12 = n

PV = $42,852• Determine the outstanding balance on new loan at the end of 10

years.

$461.05 = PMT

10.5/12 = i

15 x 12 = n

PV = $41,709

Lump sum saving=42,852-$41,709=$1,143

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Determine Present Value of Savings1. PV of monthly savings

$53.25 = PMT

13 /12 = i

10 x 12 = n

PV =$3,566

2. PV of the lump sum savings-$1,143 = FV

13 /12 = i

10 x 12 = n

PV =$313.68

Net present value=$3,566+313.68-3,907=-$27.32

Therefore, we should not refinance if we plan to hold the mortgage for only 10 years.

Question: Find the holding period that has NPV=0.

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Refinancing

Summary:• Find present value of savings• Subtract cost from PV of savings• If positive NPV refinance• If negative NPV do not refinance

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Capital budgeting and risk

• Basic formula - CAPM adjusts risk-premium for project beta

• Note that what is relevant is the project beta, and not the beta of the company as a whole.

))(()( fmAfA rrErrE

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Weighted Average cost of Capital

• For projects that have the same risk as the company’s existing business, the company’s cost of capital is the correct discount rate.

rasset=D/Vrdebt+E/Vrequity

asset=D/V debt+E/V equity

Example:

debt=0.2, equity=1.2, D?V=0.4, E/V=0.6, rf=6.6%, rm=13.6%

1. asset=0.8, rasset=6.6%+0.8(13.6%-6.6%)=12.2%

or, 2. rdebt=8%,requity=15%, rasset=0.4*8%+0.6*15%=12.2%