Module 1 Finance
Firm Value:
The value of the firm is the risk adjusted present value of the expected future free cash
flow (FCF)
The sum of the value of the firm’s equity and the value of the debt
Firm value is measured as the present value of the Operating Free Cash Flows (OFCF)
Firm Value (V) = t=1 OFCFt
(1+ WACC)t
V= Value of the firm
OFCF = Operating free cash flows (after tax)
WACC= weighted average cost of capital
OFCF = Revenue – Operating Expenses – Capital Expenditure
WACC = re E/V + rd (1-t) D/V V=E+D
Re = cost of equity E/V = Percentage of equity financing
Rd= cost of debt D/V = Percentage of debt financing
E= value of firm’s equity T = tax rate
D= value of firm’s debt V= OFCF/WACC Expressed as a perpetuity
Time Value of Money (TVM)
Money available at the present time is worth more than the identical sum in the future
due to its earning capacity
“present discount rate”
Future Value (FV)
What the value at a future date would be for a series of periodic payments
Relates to future investment cash inflows from investing TODAY’s money or future
payment outflows from borrowing todays money
FV = PV x ( 1 + r)n
FV = future value of money
PV = present value of money
R = interest rate
N = number of compounding periods per year
T = number of years
Example: Place 1500 into an account earning 6%. How much will be in the account after 7
years?
FV(n) = PV x (1 +r)n n=7, i=6, pv=-1500, pmt=0,
FV = 1500 x ( 1 + 0.06)7 solve for FV.
, FV = 1500 x 1.50363
FV = 2255.445
Excel: =FV(0.06,7,0,1500)
Present Value (PV)
The current worth of a future sum of money or stream of cash flows given in a
specified rate of return
Future cash flows are discounted at the discount rate: the higher the discount rate,
the lower the PV of the future cash flows
PV = FVn/ (1 + r)n
Used To find the value of the future sums in present day dollars
Example: I have created a legal contract that promises to pay the holder 10,000 in 9 years. What
price would you be willing to pay for the contract now to provide a return of 7%?
PV = FV (n) / (1+ r)n
PV = 10000/ ( 1 + 0.07)9 N=9, i=7, pmt=0, fv=10000,
PV = 10000/1.079 solve for pv
PV = 10000/ 1.83846
PV = 5439.3374
Excel: = PV(0.07,9,0,10000)
Practice: What if we only get the 100 once at the end of this year? (fair rate is 8%)
PV= FVn / (1 + r)n
PV = 100 / (1+0.08)1
PV = 92.59
Excel =pv(.08,1,100 ,0)
Practice: What if we get it once, at the end of ten years? (fair rate is 8%)
PV = FVn/(1+r)n
= 100/ (1 + 0.08)10
= 46.319
PV is used to find unequal cash flow
Example: I have just signed a contract that will pay me 100 at the end of this year, 150 the year
after, and 200 at the end of the third year. If the fair rate is 4%, what is this contract worth now?
Find the PV of each and add them up:
PV = FV/ ( 1+ r)n
= 100/ 1+ 0.04 1 + 150/ 1 +0.04 2 + 200/ 1 + 0.043 = 412.6365
Solve for NPV
NPV= Net Present Value. This is the difference between the present value of cash
inflows and the present value of cash outflows. The Time value of money is taken into
consideration.
, Example: If I loan you 1500 now and you repay me with a single 2000 payment in two years,
what rate will I earn? Find the interest rate
FV = PV x (1 + r)n
FV/PV – 1 = rn N=2, pv=-1500, pmt=0, fv=2000, solve for i
2
(2000/1500) – 1 = r
R = (2000/1500) – 1
R = 0.1547
Excel = RATE (2,0,1500,-2000)
Example: Place 5000 in an account that earns 6%. How long will it take to grow to 7500?
Finding “n-times”
FV = PV x ( 1+r)n i=6, PV=-5000, pmt=0, fv=7500, solve for n
7500 = 5000 x (1 + 0.06)n
7500 = 5000 x 1.06n
7500/5000 = 1.06n
1.5 = 1.06n
Ln 1.5 = ln 1.06 x n
0.4055 = n x 0.0583
6.955 = n
Excel: =NPER(0.06,0,5000,-7500)
Practice: Put 1200 in an account earning 6%. How long until it grows to 2000?
FV = PV x (1+r)n
2000 = 1200 x (1+ 0.06)n
2000 = 1200 x 1.06n
2000/1200 = 1.06n
1.67 = 1.06n
Ln 1.67 = ln 1.06 x n
0.513/ 0.058 = n
8.7667 = n
Practice: Buy a new calculator for 400. Leave it in the original wrapping for six years. Sell it to a
finance nerd for 600 at that point. What is your rate of return?
FV = PV x (1+r)n
1/n
FV/PV – 1 = r
(600/400)1/6 – 1 = r
(1.5)1/6 – 1 = r
1.0699 – 1 = r
0.0699 = r multiply by 100 to get percentage
0.0699 x 100 = 6.9%
Firm Value:
The value of the firm is the risk adjusted present value of the expected future free cash
flow (FCF)
The sum of the value of the firm’s equity and the value of the debt
Firm value is measured as the present value of the Operating Free Cash Flows (OFCF)
Firm Value (V) = t=1 OFCFt
(1+ WACC)t
V= Value of the firm
OFCF = Operating free cash flows (after tax)
WACC= weighted average cost of capital
OFCF = Revenue – Operating Expenses – Capital Expenditure
WACC = re E/V + rd (1-t) D/V V=E+D
Re = cost of equity E/V = Percentage of equity financing
Rd= cost of debt D/V = Percentage of debt financing
E= value of firm’s equity T = tax rate
D= value of firm’s debt V= OFCF/WACC Expressed as a perpetuity
Time Value of Money (TVM)
Money available at the present time is worth more than the identical sum in the future
due to its earning capacity
“present discount rate”
Future Value (FV)
What the value at a future date would be for a series of periodic payments
Relates to future investment cash inflows from investing TODAY’s money or future
payment outflows from borrowing todays money
FV = PV x ( 1 + r)n
FV = future value of money
PV = present value of money
R = interest rate
N = number of compounding periods per year
T = number of years
Example: Place 1500 into an account earning 6%. How much will be in the account after 7
years?
FV(n) = PV x (1 +r)n n=7, i=6, pv=-1500, pmt=0,
FV = 1500 x ( 1 + 0.06)7 solve for FV.
, FV = 1500 x 1.50363
FV = 2255.445
Excel: =FV(0.06,7,0,1500)
Present Value (PV)
The current worth of a future sum of money or stream of cash flows given in a
specified rate of return
Future cash flows are discounted at the discount rate: the higher the discount rate,
the lower the PV of the future cash flows
PV = FVn/ (1 + r)n
Used To find the value of the future sums in present day dollars
Example: I have created a legal contract that promises to pay the holder 10,000 in 9 years. What
price would you be willing to pay for the contract now to provide a return of 7%?
PV = FV (n) / (1+ r)n
PV = 10000/ ( 1 + 0.07)9 N=9, i=7, pmt=0, fv=10000,
PV = 10000/1.079 solve for pv
PV = 10000/ 1.83846
PV = 5439.3374
Excel: = PV(0.07,9,0,10000)
Practice: What if we only get the 100 once at the end of this year? (fair rate is 8%)
PV= FVn / (1 + r)n
PV = 100 / (1+0.08)1
PV = 92.59
Excel =pv(.08,1,100 ,0)
Practice: What if we get it once, at the end of ten years? (fair rate is 8%)
PV = FVn/(1+r)n
= 100/ (1 + 0.08)10
= 46.319
PV is used to find unequal cash flow
Example: I have just signed a contract that will pay me 100 at the end of this year, 150 the year
after, and 200 at the end of the third year. If the fair rate is 4%, what is this contract worth now?
Find the PV of each and add them up:
PV = FV/ ( 1+ r)n
= 100/ 1+ 0.04 1 + 150/ 1 +0.04 2 + 200/ 1 + 0.043 = 412.6365
Solve for NPV
NPV= Net Present Value. This is the difference between the present value of cash
inflows and the present value of cash outflows. The Time value of money is taken into
consideration.
, Example: If I loan you 1500 now and you repay me with a single 2000 payment in two years,
what rate will I earn? Find the interest rate
FV = PV x (1 + r)n
FV/PV – 1 = rn N=2, pv=-1500, pmt=0, fv=2000, solve for i
2
(2000/1500) – 1 = r
R = (2000/1500) – 1
R = 0.1547
Excel = RATE (2,0,1500,-2000)
Example: Place 5000 in an account that earns 6%. How long will it take to grow to 7500?
Finding “n-times”
FV = PV x ( 1+r)n i=6, PV=-5000, pmt=0, fv=7500, solve for n
7500 = 5000 x (1 + 0.06)n
7500 = 5000 x 1.06n
7500/5000 = 1.06n
1.5 = 1.06n
Ln 1.5 = ln 1.06 x n
0.4055 = n x 0.0583
6.955 = n
Excel: =NPER(0.06,0,5000,-7500)
Practice: Put 1200 in an account earning 6%. How long until it grows to 2000?
FV = PV x (1+r)n
2000 = 1200 x (1+ 0.06)n
2000 = 1200 x 1.06n
2000/1200 = 1.06n
1.67 = 1.06n
Ln 1.67 = ln 1.06 x n
0.513/ 0.058 = n
8.7667 = n
Practice: Buy a new calculator for 400. Leave it in the original wrapping for six years. Sell it to a
finance nerd for 600 at that point. What is your rate of return?
FV = PV x (1+r)n
1/n
FV/PV – 1 = r
(600/400)1/6 – 1 = r
(1.5)1/6 – 1 = r
1.0699 – 1 = r
0.0699 = r multiply by 100 to get percentage
0.0699 x 100 = 6.9%
