fundamentals of corporate finance chapter 5 discounted cash flow valuation
TRANSCRIPT
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Fundamentals of Corporate Finance
Chapter 5
Discounted Cash Flow Valuation
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Overview of Lecture
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Corporate Finance in the News
Insert a current news story here to frame the material you will cover in the lecture.
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Future Value with Multiple Cash Flows
Suppose you deposit €100 today in an account paying 8 per cent. In one year, you will deposit another €100. How much will you have in two years?
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Future Value with Multiple Cash Flows
Consider the future value of €2,000 invested at the end of each of the next five years. The current balance is zero, and the rate is 10 per cent.
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Future Value with Multiple Cash Flows
Consider the future value of €2,000 invested at the end of each of the next five years. The current balance is zero, and the rate is 10 per cent.
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Example 5.1Saving Up Once Again
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Example 5.1Saving Up Once Again
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Present Value with Multiple Cash Flows
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Present Value with Multiple Cash Flows
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Example 5.2How Much is it Worth?
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Example 5.2How Much is it Worth?
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Example 5.3How Much is it Worth Part 2?
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Example 5.3How Much is it Worth Part 2?
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Spreadsheet Strategies
Now that the students have got a good idea how to do PV and FV calculations, spreadsheets should be covered now to illustrate how they can be used for these types of problems.
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Cash Flow Timing
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Valuing Level Cash Flows: Annuities and Perpetuities
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Present Value for Annuity Cash Flows
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Present Value for Annuity Cash Flows
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PV of an Annuity Formula
1 Present value factorAnnuity present value =
1 [1 / (1 ) ]
1 1
(1 )
t
t
Crr
Cr
Cr r r
The present value of an annuity of £C (or any other currency) per period for t periods when the rate of return or interest rate is r is given by:
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Example 5.4How Much Can You Afford?
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Example 5.4How Much Can You Afford?
The loan payments are in ordinary annuity form, so the annuity present value factor is:
Annuity PV factor = (1 Present value factor)/r = [1 (1/1.0148)]/.01 = (1 .6203)/.01 = 37.9740
With this factor, we can calculate the present value of the 48 payments of €632 each as:
Present value = €632 37.9740 = €24,000
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Table 5.1Annuity Present Value Interest Factors
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Spreadsheet Strategies
Show how to use a spreadsheet to calculate the present value of an annuity
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Example 5.5Finding the Number of Payments
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Example 5.5Finding the Number of Payments
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Future Value of Annuities
Annuity FV factor = (Future value factor 1) /[(1 + ) 1] /(1 ) 1
t
t
rr rr
r r
(1 ) 1FV of Annuity
trC
r r
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Annuities Due
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Perpetuities
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Perpetuities
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Preference Shares
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Example 5.6Preference Shares
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Example 5.6Preference Shares
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Growing Annuities
11
1Growing annuity present value
tgrC
r g
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Growing Perpetuities
1Growing perpetuity present value
CC
r g r g
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Comparing Rates
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Comparing Rates
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Comparing Rates
12
12
EAR = [1 + (Quoted rate/ )] 1= [1 + (.12/12)] 1= 1.01 1= 1.126825 1= 12.6825%
mm
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Example 5.7What’s the EAR?
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Example 5.7What’s the EAR?
The bank is effectively offering 12%/4 = 3% every quarter. If you invest £100 for four periods at 3 per cent per period, the future value is:
4
£=£=
Future value = £100 1.03100 1.1255112.55
The EAR is 12.55 per cent: £100 (1 + .1255) = £112.55.
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Example 5.7What’s the EAR?
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Example 5.8Quoting a Rate
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Example 5.8Quoting a Rate
12
12
EAR = [1 + (Quoted rate/ )] 1.18 = [1 + ( /12)] 1
1.18 = [1 + ( /12)]
mmqq
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The Annual Percentage Rate
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The Annual Percentage Rate
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Example 4.14: APR
The sale price of a car is £30,000.
The quoted rate is “a simple annual interest rate of 12 percent on the original borrowed amount over three years, payable in 36 monthly installments.”
The finance company also charges an administration fee of £250. What does this mean?
The lender will charge 12 percent interest on the original loan of £30,000 every year for three years.
Each year, the interest charge will be (12% of £30,000) £3,600 making a total interest payment of £10,800 over three years.
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Example 4.14: APR
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Example 4.14: APR
What is the APR of this loan?
This gives an Annual Percentage Rate (APR) of 24.13%!
The lender must also state the total amount paid at the end of the loan, which, in this case, is £41,049.88 and the total charge for credit is £11,049.88 (£41,049.88 - £30,000).
1 2 36
12 12 12
£1,133.33 £1,133.33 £1,133.33£30,000 £250
(1 APR) (1+APR) (1+ APR)
L
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Continuous Compounding
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Continuous Compounding Formula
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Loan Types and Loan Amortization
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Example 5.10Treasury Bills
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Example 5.10Treasury Bills
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Example 5.10Treasury Bills
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Example 5.10Treasury Bills
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Example 5.10Treasury Bills
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Spreadsheet Strategies
You should now take the students through some examples on the spreadsheet.
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Activities for this Lecture
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Thank You