Prep
Session 2
Capital
Budgeting
Time Value of
Money
▶ A dollar today is worth more than a dollar tomorrow
▶ The same amount of money becomes less valuable as time passes due to –
▪ Opportunity Cost (Potential of Earning Positive Returns)
▪ Inflation
▪ Uncertainty
▶ Factors affecting the erosion of value due to time –
▪ Interest Rate
▪ Time Period
Time Value of
Money FV = PV x [ 1 + (i / n) ] (n x t) Here,
▪ FV = Future Value
▪ PV = Present Value
▪ n = Number of compounding periods per year
▪ t = Number of years
▶ Compounding – Calculating FV from a given PV
▶ Discounting – Calculating PV from a given FV
▶ TVM is used extensively in Loan Amortization, Capital Budgeting,
Valuation Methodologies, Trading, etc.
▶ Common Variations used – Annuity, Continuous Compounding
TVM Examples
▶ Assume a sum of $10,000 is invested for one year at 10% interest
compounded annually. The future value of that money is:
FV = 10,000* (1+10%) = $11,000
• Quarterly Compounding: FV = $10,000 x [1 + (10% / 4)] ^ (4 x 1) = $11,038 •
Monthly Compounding: FV = $10,000 x [1 + (10% / 12)] ^ (12 x 1) = $11,047 •
Daily Compounding: FV = $10,000 x [1 + (1g0% / 365)] ^ (365 x 1) = $11,052
▶ Present Value of sum compounded annually at 7% interest that would
be worth $5,000 one year from today is:
PV = $5,000 / (1 + 7%) = $4,673
Capital Budgeting
▶ Capital budgeting refers to the decision-making process that companies follow
with regard to which capital-intensive projects they should pursue.
▶ Such capital-intensive projects could be anything from opening a new factory to a
significant workforce expansion, entering a new market, or the research and
development of new products.
▶ Capital budgeting decisions are based on incremental after-tax cash flows
discounted at the opportunity cost of capital.
Some important concepts
▶ Incremental cash flow is the net cash flow attributable to an investment project. It represents
the change in the firm's total cash flow that occurs as a direct result of accepting the project
▶ A sunk cost is a cost that has already occurred and cannot be recovered by any means. Sunk costs
are independent of any event and should not be considered when
making investment or project decisions. Only relevant costs (costs that relate to a specific decision
and will change depending on that decision) should be considered when making such decisions
▶ Independent versus mutually exclusive projects - Mutually exclusive are investments that
compete in some way for a company's resources - a firm can select one or another but not
both. Independent projects, on the other hand, do not compete with the firm's resources. A
company can select one or the other or both, so long as minimum profitability thresholds are
met.
Net Present
Value
▶
This method discounts all cash flows (including both inflows and outflows) at the
project's cost of capital and then sums those cash flows. The project is accepted if
the NPV is positive.
▶ NPV =σ ������
(1+��)^��
Where CFt is the expected cash flow at period t, k is the project's cost of
capital
▶ Decision rules
1. The higher the NPV, the better.
2. Reject if NPV is less than or equal to 0
Illustration
Cashflows (CFt)
Year (t) Project A Project B 0 -5,000 -5,000 1 750 500 2 2000
1500 3 2000 2000 4 2500 3000
▶ Assuming the cost of capital for the firm is 10%, calculate each cash flow by
dividing the cash flow by (1 + k)^t where k is the cost of capital and t is the year
number.
Calculate the NPV for Project A and B above.
▶ NPV = CF0 + CF1 + CF2 + CF3 + CF4
▶ Project A's NPV = −5,000 +750 +2000 +2000 +2500 = $549 1.1
1.121.131.14
▶ Project B's NPV = −5,000 +500 +1500 +2000 +3000 = $246 1.1
1.121.131.14
Internal Rate of Return
(IRR)
▶ It is the discount rate at which a project's NPV is equal to
zero.
������
σ
=0
▶ NPV = (1+������)^��
▶ Note this formula is simply the NPV formula solved for the particular discount rate
that results in NPV to equal zero. The IRR on a project is its expected rate of
return.
▶ The NPV and IRR methods will usually lead to the same accept or reject
decisions.
▶ Decision rules
1. The higher the IRR, the better.
2. Define the hurdle rate, which typically is the cost of capital.
3. Reject if IRR is less than or equal to the hurdle rate.
Illustration
Cashflows (CFt)
Year (t) Project A Project B 0 -5,000 -5,000 1 750 500 2 2000 1500 3
2000 2000 4 2500 3000▶ Project A’s IRR can be calculated by solving the
following equation −5,000 + 750 + 2000 + 2000 + 2500 = 0
(1+������) (1+������)2(1+������)3(1+������)4
▶ Since it is difficult to determine the IRR by hand, the use of a financial
calculator is needed to solve for IRR.
▶ The IRR for Project A is 14% and for Project B is 12%
Conflict between
NPV and IRR
timing
Case 1: Different cashflow pattern
and
Cashflows (CFt)
Year (t) Project A Project B 0 (5,000) (5,000) 1 2,000 0 2 2,000 0 3
2,000 0 4 2,000 0 5 2,000 15,000 NPV 2,581.57 4,313.82 IRR 29% 25% ▶
Solution: Project B i.e. project with a higher NPV is chosen.
▶ Reason: In the NPV calculation, the implicit assumption for reinvestment
rate is 10% Is present
Conflict between
NPV and IRR
Case 2: Different size and
investment of project
Cashflows (CFt)
Year (t) Project A Project B 0 (5,000) (20,000) 1 2,000 7,000 2
2,000 7,000 3 2,000 7,000 4 2,000 7,000 5 2,000 7,000 NPV 2,581.57
6,535.51 IRR 29% 22% ▶ Solution: Project B i.e. project with a higher NPV is
chosen.
▶ Reason: In the NPV calculation, the implicit assumption for reinvestment
rate is 10% Is present
Payback
Period
▶ It is the expected number of years required to recover the original investment. ▶
Payback occurs when the cumulative net cash flow equals 0 ▶ Decision rules
• The shorter the payback period, the better.
• A firm should establish a benchmark payback period. Reject if payback is greater
than benchmark.
▶ Drawbacks
• It ignores cash flows beyond the payback period. Payback period is a type of "break
even" analysis: it cares about how quickly you can make your money to recover the
initial investment, not how much money you can make during the life of the
project.
• It does not consider the time value of money. Therefore, the cost of capital is not
reflected in the cash flows or calculations.
Illustration
When a firm is embarking upon a project, it needs tools to assist in making the decision of whether to
invest in the project or not. In order to demonstrate the use of these four methods, the cash flows
presented below will be used
Cashflows (CFt)
Year (t) Project A Project B 0 (1,000) (1,000) 1 750 100
2 350 250
3 150 450
4 50 750
Illustration
Project A Project B
CF Cumulative CF CF Cumulative CF
Year (t)
0 (1,000) (1,000) (1,000) (1,000) 1 750 (250) 100 (900) 2 350 100 250 (650) 3 150 250 450
(200) 4 50 300 750 550
We see that in case of project A, the cumulative cashflows reach 0 between
time 1 and 2. Thus, by simple interpolation,
����− 1 0 − −250
2 − 1=100 − −250
Solving the eqn, PP = 1.71 years
Similarly, payback period for project B is 3.27 years
Discounted Payback
Period
▶ It is similar to the regular payback method except that it discounts cash flows
at the project's cost of capital. It considers the time value of money, but it
ignores cash flows beyond the payback period.
Illustration
Year
(t)
Discounted CF Discounted
Project A
CF
0
(1,000)
Cum. CF
Project B
CF Discounted CF Discounted Cum. CF
(1,000) (1,000) (1,000) (1,000) (1,000)
1 750 750/1.1 = 681 (319) 100 100/1.1 = 91 (909) 2 350 350/1.12 = 289 (30) 250 250/1.12 = 207 (702) 3 150 150/1.13 = 113 83
450 450/1.13 = 338 (364) 4 50 50/1.14 = 34 117 750 750/1.14 = 512 148
We see that in case of project A, the discounted cumulative cashflows reach 0 between time 2 and 3.
Thus, by simple interpolation,
������− 2 0 − −30
3 − 2=83 − −30
Solving the eqn, PP = 2.26 years
Similarly, discounted payback period for project B is 3.71 years
Profitability Index
▶ This is an index used to evaluate proposals for which net present values have been
determined. The profitability index is determined by dividing the present value of each
proposal by its initial investment.
▶ PI = PV of future cash flows / Initial investment = 1 + (NPV / Initial investment) ▶ The PI
indicates the value you are receiving in exchange for one unit of currency invested.
▶ An index value greater than 1.0 is acceptable and the higher the number, the more
financially attractive the proposal.
▶ A ratio of 1.0 is logically the lowest acceptable measure on the index. Any value lower than 1.0
would indicate that the project's PV is less than the initial investment.
Common Questions/ Topics
Understanding the 3
Financial Statements
▶ Impact on the three financial statements if depreciation
increases by $10
▶ Impact on three financial statements if a machine of
$100
Qis sold for uestion 1 $80 Amount ($)
Decrease in Operating Income -10
Question 2 Amount ($) Decrease in Other
Income (Loss) -20
Decrease in Net Income (Tax – Decrease in Net Income (Tax – -16
20%)
30%*) -7 Decrease in N.I -7
Balance Sheet (PPE, Cash) -10+3 = -7
Increase in Dep (Non Cash) +10 Increase in
Operating CF +3 Balance Sheet (Liabilities) -7
Decrease in N.I -16 Increase in Loss (Non
Operating) +20 Increase in Operating CF +4
Increase in Investing CF +80 Balance Sheet
(Liabilities) -16 Balance Sheet (PPE, Cash) -100+84
= -16
Operating & Financial Leverage
▶ What is operating and financial leverage? ▶
Impact of Fixed Assets on Profits
▶ Operating Leverage – Impact on Operating Income due to Change in Sales
(Lever: Fixed Cost)
▶ DOL = Contribution/(Contribution – Fixed Cost)
= %Δ in EBIT/%Δ in Sales
▶ on Net Income due to change in Capital Structure (Lever: Debt
component in capital)
▶ DFL = EBIT/(EBIT – Finance Cost)
=%Δ in EPS/%Δ in EBIT
▶ Extra: DuPont Analysis
Minority Interest
▶ What is minority interest and how does it reflect in the
financial statements?
▶ Definition – Ownership of less than 50% of an enterprise.
▶ Financial Statements – Equity and Income attributable to
the minority shareholders of a company shows up
separately in the Equity (IFRS, GAAP) or NCL (GAAP) of the
consolidated statement of the parent company.
Financial Ratios
▶ Which financial ratio will you look at if you want to
know about the health of a company
▶ Name 5 financial ratios you would look at to judge a
manufacturing company
More Questions
(Corporate Finance/Accounting)
✔ Explain IFRS-16/INDAS-116, how it has changed
accounting?
• Lease accounting
✔ What is the effect of taking more debt on Cost of
capital (WACC)? Does WACC change proportionally?
• Modigliani & Miller theory
✔ Can Beta be negative? If yes, then in what scenarios? •
Gold