Finance - Discount Cash Flow

[Excel File]

Discount Cash Flow
FV = PV(1 + r)^t
PV = FV /(1+r)^t
r = ( (FV/PV)^1/t )-1
Perpetuity	PV = C/r
Consider a Perpetuity paying $110 a year. If the interest rate is 7.5% what is the value?
	C	110
	r	0.075
	PV	1466.666667	=D11/D12
Growing Perpetuity	PV = C/(r - g)
A corporation is just about to pay a $2 dividend per share. Investors expect the dividend to rise by 5%
Discount rate is 10%. What is the price of the stock?
(Initial dividend needs to be added)	C	2
(Next year's dividend needs to be added)	r	0.1
(Next year's dividend x 1+ g)	g	0.05
	PV	44	=D21+(D21*(1+D23))/(D22-D23)
Continuous Compounding	PV = PVe^rt (E is euler number, use EXP in Excel)
Present Value of an Annuity (PVIFArt)	PV = C[(1-(1/(1+r)^t)/r]
Bob won the lottery, which pays 50,000/year for 20 years. He will receive his first payment a year from now.
If the interest rate is 8%, what is the value of the money?
C is negative to indicate the money is being received	C	-50000
Otherwise answer shows negative.	t	20
	r	0.08
	PV	490,907.37	=PV(D41,D40,D39,,0)
If Bob reeceives a payment immediately, what is the value?
	Pmt year 0	50000
	t	19
	r	0.08
	PV	$530,179.96	=D47+PV(D49,D48,-D47)
Present Value of a Growing Annuity	PV = c[(1/(r-g))-1/(r-g) x ((1+g)/(1+r)^t
Bob gets a job paying 80k per year. He anticipates a 9% raise per year for the next 40 years.
If the interest rate is 20% what is the value of his lifetime salary?
	C	80000
	r	0.2
	g	0.09
	t	40
	PV	$711,730.71	=D59*(1-((1+D61)/(1+D60))^D62)/(D60-D61)
Retirement
How much will you have in 30 years if every year you put $3,000 into a retirement account that pays 6% per year.
(PMT in formula is negative)	C	3000
	t	30
	r	0.06
	FV	$237,174.56	=FV(D72,D71,-D70)
Bob will receive a four year annuity of $500 per year, beginning at date 6.
If interest is 6%, what is the present value?
Step 1 (Calculate at date 5)	C	500
	r	0.1
	t	4
	PV	$1,584.93	=PV(D84,D85,-D83)
Step 2 (Return Value at date 0)	FV	$1,584.93
	r	0.1
	t	5
	PV	$984.12	=PV(D90,D91,,-D89,)
A family expects college expenses of 30,000 per year for their kid.
They have 18 years to save and expect a 14% return.
They will withdraw the money over four years.
Step 1 Calculate the PV of the four years	C	30000
	r	0.14
	t	4
	pv	-$87,411.37	=PV(D101,D102,D100)
Step 2 Return this to date 0	C	-$87,411.37
	r	0.14
	t	17
	pv	$9,422.92	=PV(D108,D109,,D107)
Step 3  Calculate annual deposits	PMT	-$1,478.60	=PMT(D108,D109,D111)
Present Value Discount Loan
Loan Amount	25000
Time	5
Interest	0.12
PV	-$14,185.67	=PV(C121,C120,,C119)
Firm Valuation
A company is investing $1M in four new locations.
Cash flows of 200k are expected for 9 years.
Discount rate is .15	PMT	200,000.00
What is the NPV?	t	9
	r	0.15
	Invest	-1,000,000.00
(PMT is negative because we are receiving the pmt)		-$45,683.22	=PV(D132,D131,-D130)+D133
	(PV of inflow is	$954,316.78