NPV and Debt
Assume:
Long-term debt at 4.25% = $2,000
A/P = $300
N/P = $400
100 shares selling for $25 each
A 3-year project
Pro forma income statement for a 3-year project (S = $2,000)
Today
1
2
3
Sales
(Costs)
(Depreciation)
EBIT
(Interest)
EBT
(Tax)
Net income
$0.00
$0.00
$300.00
-$300.00
$0.00
-$300.00
$0.00
-$300.00
$5,000.00
$3,500.00
$540.00
$960.00
$85.00
$875.00
$297.50
$577.50
$5,000.00
$3,500.00
$432.00
$1,068.00
$85.00
$983.00
$334.22
$648.78
$5,000.00
$3,500.00
-$272.00
$1,772.00
$85.00
$1,687.00
$573.58
$1,113.42
Addition to RE
Dividend
-$300.00
$0.00
$375.38
$202.13
$421.71
$227.07
$723.72
$389.70
1
Pro forma income statement for a 3-year project (S = $2,000)
Today
1
2
3
Cash
Inventory
A/R
Current assets
$100.00
$500.00
$400.00
$1,000.00
$1,015.38
$500.00
$400.00
$1,915.38
$1,869.09
$500.00
$400.00
$2,769.09
$0.00
$0.00
$0.00
$0.00
Gross fixed assets
Depreciation
Net fixed assets
$3,000.00
$300.00
$2,700.00
$3,000.00
$840.00
$2,160.00
$3,000.00
$1,272.00
$1,728.00
$1,000.00
$1,000.00
$0.00
Total assets
$3,700.00
$4,075.38
$4,497.09
$0.00
Today
1
2
3
$300.00
$400.00
$700.00
$300.00
$400.00
$700.00
$300.00
$400.00
$700.00
$0.00
$0.00
$0.00
Long-term debt
$2,000.00
$2,000.00
$2,000.00
$0.00
Outstanding shares
Retained earnings
Owner's equity
$1,300.00
($300.00)
$1,000.00
$1,300.00
$75.38
$1,375.38
$1,300.00
$497.08
$1,797.08
$0.00
($0.00)
($0.00)
Total L&E
$3,700.00
$4,075.38
$4,497.08
($0.00)
A/P
N/P
Current liabilities
2
Cash flow projection for a 3-year project (S = $2,000)
Today
1
2
3
-$300.00
$300.00
$0.00
$633.60
$540.00
$1,173.60
$704.88
$432.00
$1,136.88
$1,169.52
-$272.00
$897.52
Sales
Costs
Tax**
OCF
$0.00
$0.00
$0.00
$0.00
$5,000.00
$3,500.00
$326.40
$1,173.60
$5,000.00
$3,500.00
$363.12
$1,136.88
$5,000.00
$3,500.00
$602.48
$897.52
ATNOR
DeprTS
OCF
$0.00
$0.00
$0.00
$990.00
$183.60
$1,173.60
$990.00
$146.88
$1,136.88
$990.00
-$92.48
$897.52
OCF
Net Capital Spending
Investment in CA net of A/P
$0.00
-$3,000.00
-$700.00
$1,173.60
$0.00
-$915.38
$1,136.88
$0.00
-$853.71
$897.52
$2,000.00
$2,469.09
Unlevered Cash Flow
-$3,700.00
$258.23
$283.17
$5,366.61
$0.00
$28.90
$28.90
$28.90
CF from assets
-$3,700.00
$287.13
$312.07
$5,395.51
CF to creditors
CF to shareholders
-$2,400.00
-$1,300.00
$85.00
$202.13
$85.00
$227.07
$2,485.00
$2,910.51
CF to stakeholders
-$3,700.00
$287.13
$312.07
$5,395.51
Unlevered Net Income
Depreciation
OCF
Interest tax shield
3
Things to note:
Notes payable carry very low interest, almost zero. For the purpose of this exercise we will assume to
be equal to zero. The cost of long-term borrowing is 4.25%. The effective cost of borrowing, however,
becomes:
Effective cost of borrowing = Interest paid/All liabilities
Effective cost of borrowing = $85/($2,000 + $400 + $300) = 3.15%
At t= 0, Toy Inc requires $3,000 worth of plant and equipment and $1,000 worth of current assets.
Since current assets are partially financed with accounts payable ($300), the total initial investment
outlay that needs debt and equity financing is:
Initial investment outlay = $3,000 + $1,000 - $300 = $3,700
OCF requires the estimation of unlevered net income. For example, in year 1, net income is equal to
$577.5 as shown in the pro-forma income statement. One would have to estimate unlevered net income
in the following way:
UNI = EBIT(1-Tax%) - $960(1-0.34) = $633.6
The tax shield is equal to:
Annual tax shield = Annual interest(Tax%) = $85(0.34) = $28.9
4
M&M NPV
M&M states that:
Total market value of project = PV(unlevered cash flow) + PV(debt tax shield)
or
Market value of equity + Market value of liabilities = PV(unlevered cash flow) + PV(debt tax shield)
or
Market value of equity = - Market value of liabilities + PV(unlevered cash flow) + PV(debt tax shield)
M&M NPV can be derived from above:
NPV = Total market value of project – Initial cost
NPV = PV(unlevered cash flow) + PV(debt tax shield) – Initial cost
In this case, NPV is calculated by discounting unlevered cash flows using the unlevered cost of equity;
and by discounting the annual tax shield at the effective cost of debt.
PV(debt tax shield at 3.15%) = $81.51
M&M NPV = $258.23/(1.05) + $283.17/(1.05)2 + $5,366.61/(1.05)3 + $81.51 - $3,700 = $1,520.17
Further implications:
Fair market value of equity = PV(unlevered cash flow) + PV(debt tax shield) - Total liabilities
= $258.23/(1.05) + $283.17/(1.05)2 + $5,366.61/(1.05)3 + $81.51 -$2,700 = $2,520.17
5
Flow to equity
NPV = PV(cash flow to shareholders) – Initial equity investment
Note that PV(cash flow to shareholders) is estimated using the levered cost of equity
Levered cost of equity = Unlevered cost of equity +Risk premium(financial leverage)
Which financial leverage?
Book value leverage = $2,700/$1,000 = 2.7
Market value leverage (current prices) = $2,700/$2,500 = 1.08
or
Market value leverage (estimated fair value) = $2,700/ 2,520.17= 1.07
Hypothetical levered cost of equity = 6.32%
Flow to equity NPV = $202.13/(1.0632) +$227.07/(1.0632)2+$2,910.15/(1.0632)3 - $1,300 = $1,512.7
WACC NPV
NPV = PV(unlevered CF) – Initial cost
Note:
In this case, the present value of the project is found by discounting unlevered cash flow using the
wacc.
Wacc = (Levered cost of equity)(weight of equity) + (Effective cost of debt)(1-Tax%)(weight of debt)
Assume weights are given by market prices:
wacc = 6.32%(0.4808) + 3.15%(0.5192)(1-0.34) = 4.12%
WACC NPV = $258.23/(1.0412) + $283.17/(1.0412)2 + $5,366.61/(1.0412)3 - $3,700 = $1,563.6
6
Perpetual project
Toy Inc.: Sales projection with debt financing
Today
1
2
3
Sales
(Costs)
(Depreciation)
EBIT
(Interest)
EBT
(Tax)
Net income
$0.00
$0.00
$300.00
-$300.00
$0.00
-$300.00
$0.00
-$300.00
$5,000.00
$3,500.00
$540.00
$960.00
$85.00
$875.00
$297.50
$577.50
$5,000.00
$3,500.00
$432.00
$1,068.00
$85.00
$983.00
$334.22
$648.78
$5,000.00
$3,500.00
$345.60
$1,154.40
$85.00
$1,069.40
$363.60
$705.80
Addition to RE
Dividend
-$300.00
$0.00
$375.38
$202.13
$421.71
$227.07
$458.77
$247.03
7
Toy Inc pro-forma balance sheet with $2,000 long-term debt, $300 A/P, and $400 N/P
Today
1
2
3
Cash
Inventory
A/R
Current assets
$100.00
$500.00
$400.00
$1,000.00
$1,015.38
$500.00
$400.00
$1,915.38
$1,869.09
$500.00
$400.00
$2,769.09
$2,673.46
$500.00
$400.00
$3,573.46
Gross fixed assets
Depreciation
Net fixed assets
$3,000.00
$300.00
$2,700.00
$3,000.00
$840.00
$2,160.00
$3,000.00
$1,272.00
$1,728.00
$3,000.00
$1,617.60
$1,382.40
Total assets
$3,700.00
$4,075.38
$4,497.09
$4,955.86
Today
1
2
3
$300.00
$400.00
$700.00
$300.00
$400.00
$700.00
$300.00
$400.00
$700.00
$300.00
$400.00
$700.00
Long-term debt
$2,000.00
$2,000.00
$2,000.00
$2,000.00
Outstanding shares
Retained earnings
Owner's equity
$1,300.00
($300.00)
$1,000.00
$1,300.00
$75.38
$1,375.38
$1,300.00
$497.08
$1,797.08
$1,300.00
$955.85
$2,255.85
Total L&E
$3,700.00
$4,075.38
$4,497.08
$4,955.85
A/P
N/P
Current liabilities
8
Toy Inc.: Cash flows with debt
Today
1
2
3
-$300.00
$300.00
$0.00
$633.60
$540.00
$1,173.60
$704.88
$432.00
$1,136.88
$761.90
$345.60
$1,107.50
Sales
Costs
Tax**
OCF
$0.00
$0.00
$0.00
$0.00
$5,000.00
$3,500.00
$326.40
$1,173.60
$5,000.00
$3,500.00
$363.12
$1,136.88
$5,000.00
$3,500.00
$392.50
$1,107.50
ATNOR
DeprTS
OCF
$0.00
$0.00
$0.00
$990.00
$183.60
$1,173.60
$990.00
$146.88
$1,136.88
$990.00
$117.50
$1,107.50
OCF
Net Capital Spending
Investment in CA net of A/P
$0.00
-$3,000.00
-$700.00
$1,173.60
$0.00
-$915.38
$1,136.88
$0.00
-$853.71
$1,107.50
$0.00
-$804.37
Unlevered Cash Flow
-$3,700.00
$258.23
$283.17
$303.13
$0.00
$28.90
$28.90
$28.90
CF from assets
-$3,700.00
$287.13
$312.07
$332.03
CF to creditors
CF to shareholders
-$2,400.00
-$1,300.00
$85.00
$202.13
$85.00
$227.07
$85.00
$247.03
CF to stakeholders
-$3,700.00
$287.13
$312.07
$332.03
Unlevered Net Income
Depreciation
OCF
Interest tax shield
9
M&M NPV
M&M states that:
Total market value of project = PV(unlevered cash flow) + PV(debt tax shield)
or
Market value of equity + Market value of liabilities = PV(unlevered cash flow) + PV(debt tax shield)
or
Market value of equity = - Market value of liabilities + PV(unlevered cash flow) + PV(debt tax shield)
M&M NPV can be derived from above:
NPV = Total market value of project – Initial cost
NPV = PV(unlevered cash flow) + PV(debt tax shield) – Initial cost
In this case, NPV is calculated by discounting unlevered cash flows using the unlevered cost of equity;
and by discounting the annual tax shield at the effective cost of debt.
PV(UCF) = $258.23/(1.05) + $283.17/(1.05)2 + $303.13/(1.05)3 + $303.13(1.03)/(0.05-0.03)(1.05)3
PV(UCF) = $14,250.17
PV(debt tax shield) = $28.9/(0.0315) = $916.31
M&M NPV = $14,250.17 + $916 - $3,700 =$11.466.17
or if we want to include A/P as part of the initial cash outlay:
M&M NPV = $14,250.17+ $916 - $4,000 = $11,166.17
Further implications:
The market value of equity = - Market value of liabilities + PV(unlevered cash flow) + PV(debt tax
shield)
The fair market value of equity = -$2,700 + $14,250.17 + $916 = $12,466.17
Since the current price per share is $25, it follows that the firm is significantly undervalued
($2,500 vs $12,466.17)
Note that:
NPV = Market value of equity – Initial equity investment = $12,466.17 - $1,300 = $11,166.17
A/P lay in a grey area as they represent neither financial debt nor equity.
10
Flow to equity NPV
NPV = PV(cash flow to shareholders) – Initial equity investment
Note that PV(cash flow to shareholders) is estimated using the levered cost of equity
Levered cost of equity = Unlevered cost of equity +Risk premium(financial leverage)
Which financial leverage?
Book value leverage = $2,700/$1,000 = 2.7
Market value leverage (current prices) = $2,700/$2,500 = 1.08
Market value leverage (estimated fair value) = $2,700/$12,073.89 = 0.224
We are at a loss to estimate even a simple metric such as financial leverage!
Hypothetical levered cost of equity = 6.32%
NPV=$202.13/(1.0632) +$227.07/(1.0632)2+$247.03/(1.0632)3 +$247.03(1.03)/(0.0632-0.03)(1.0632)3
- $1,300
NPV = $5,673.35
Why such a huge discrepancy?
•Arbitrary leverage
•Inconsistent assumptions about debt levels and leverage ratios
•Lack of a reliable model to estimate discount rates
•Arbitrary growth rate in cash flows
Had we assumed 4.5% growth rate in CF to shareholders, the results would have been very close.
11
WACC NPV
NPV = PV(unlevered CF) – Initial cost
Note:
In this case, the present value of the project is found by discounting unlevered cash flow using the
wacc.
Wacc = (Levered cost of equity)(weight of equity) + (Effective cost of debt)(1-Tax%)(weight of debt)
Assume weights are given by market prices:
wacc = 6.32%(0.4808) + 3.15%(0.5192)(1-0.34) = 4.12%
NPV = $258.23/(1.0412) + $283.17/(1.0412)2 + $303.13/(1.0412)3 + $303.13(1.03)/(0.0412-0.03)
(1.0412)3 - $3,700
NPV = $21,774.85
NPV: A summary
NPV is a great tool for analysing and evaluating projects; in theory, that is. In practice, it has several
formidable challenges:
•Inability to project cash flows in the long-term
•Lack of a reliable model for predicting risk and estimating required returns
•Extreme sensitivity of NPV estimations to small changes in input variables
For short-term projections, however, NPV does a decent job.
12