Capital Investments… an introduction to finance.
• WHEN you get money is critically important. • The RISK of not getting money (or getting a different amount than expected) is critically important.
Capital Investment Decisions
• Capital Investment Decisions relate to “big projects” or “big expenditures” that you haven‟t made yet.
• We analyze whether or not the “big expenditure” is worthwhile.
Avoiding the Fixed Cost Problem
• Many measurement problems relate to fixed costs (i.e., How should we account for such costs? How should we think about them?) • This issue is not a problem for long-term capital budgeting purposes because fixed costs haven‟t happened yet…we are typically considering whether fixed investment is worthwhile.
Capital Investment:
• Three Phases of Capital Investment
1. Identification (a strategy issue)
2. Evaluation and Selection (key area)
3. Control (briefly discuss)
Evaluation and Selection
In order to establish a consistent and reasonable basis for project selection (“new opportunity” or “big expenditure” selection),
objective methods of evaluation and
selecting new opportunities are used.
Methods Discussed by Most Intro. Managerial Accounting Texts: 1. 2. 3. 4. Payback Period Accounting Rate of Return Net Present Value Internal Rate of Return
The Very Easy One
• Payback Period measures how long it takes to get your money back. You prefer investments with fast payback periods relative to those with slow payback periods. • For example, imagine that you make a $5,000 investment to buy a generic machine that will provide $1,000 worth of cash inflow for the next 10 years.
Payback Period Formula
Payback Period = Investment net annual cash inflow Payback Period = $5,000 $1,000 = 5 years All else being equal, you‟d prefer this investment to one with a 6-year payback period.
Accounting Rate of Return
• VERY Similar to R.O.I. (previously discussed) • Think of Accounting Rate of Return as being identical to ROI.
Remaining Methods Consider the Time Value of Money…this is the finance intro.
1. Net Present Value 2. Internal Rate of Return
Time Value of Money…when you get money is critical.
• Explains stories that my grandmother told me, like, “when I grew up, a cup of coffee cost 5 cents”. • Even though I‟m not that old, when I was a kid, a $100,000 house was a mansion. • In „constant value‟ terms, gasoline is not as expensive as it was in the ‟70s.
Time Value of Money
• The basic thought is that having $1 now is worth more than having $1 one year from now. • Why? If you have $1 now, at a minimum, you could put your money in the bank and earn interest. By next year, you‟ll have more than $1.
How Much More?
Suppose you put $800 in the bank and earn 5% interest. Suppose you don‟t withdraw any money. How much money will you have at the end of two years? (Yr. 1): $800 105% = $840 (Yr. 2): $840 105% = $882
How Much More?
Suppose you put $800 in the bank and earn 5% interest. Suppose you don‟t withdraw any money. How much money will you have at the end of two years?
Technically, the correct answer to “How Much More” depends on how frequently interest is “compounded.” For the purpose of this course, we‟ll assume simple compounding, meaning, it‟s valid to assume a 12% annual interest rate equals a 1% monthly interest rate.
Present Value Formulas
Suppose you put $800 in the bank and earn 5% interest (compounded annually). Suppose you don‟t withdraw any money. How much money will you have at the end of two years?
“Simple” present value formula: PV (1+ i%)n = FV You don‟t need to know formulas for the final, but $800 (1+ 5%)2 = FV they are helpful for $882 = Future Value understanding /
interpreting your results.
Present Value Formulas
Suppose you put $800 in the bank and earn 5% interest (compounded annually). Suppose you don‟t withdraw any money. How much money will you have when you retire in 55 years? The non-intuitive nature of compound interest is the basis for many financial planning „sales pitches‟.
“Simple” present value formula: PV (1+ i%)n = FV $800 (1+ 5%)55 = FV $11,708 = Future Value
Do We Want to Know Future Values?
Typically, businesses are interested in present value calculations because they want to estimate the value of future cash inflows. An unrealistic example: suppose your construction company is building a bridge. You will be paid $50 million dollars when the bridge is finished, but it will take four years to finish the bridge. What’s the present value of this payment?
The Discount Rate
(“i” in the prior problem)
• Lots of near-synonyms that accountants don‟t like to think about: interest rate, discount rate, borrowing rate, hurdle rate, cost of capital, weighted average cost of capital, hazel nuts, macadamia nuts, peanuts, etc.
• Loosely speaking, this rate – in theory – encompasses both risk and return. • Accountants like to leave this topic for finance.
The Discount Rate
• Let‟s assume a 9% discount rate… and get back to our construction problem about bridge building.
Present Value of Construction
You will be paid $50 million dollars when the bridge is finished, but it will take four years to finish the bridge. The Discount Rate is 9%.
“Simple” present value formula: PV (1+ i%)n = FV PV (1+ 9%)4 = $50,000,000 Present Value = $35,421,261
Big difference …but not terribly intuitive.
A More Realistic Example
Z company issues a bond that must be repaid in 8 years. The bond pays no interest (aka, a “zero coupon” bond), but in 8 years the company will pay the bondholder $14 million. What is the present value of the bond? It depends on the discount rate!
Assume a 9.5% discount rate.
PV (1+ i%)n = FV PV (1.095)8 = $14,000,000 PV = $6,773,530
A More Realistic Example
If the company were „less risky‟, the discount rate would be lower…investors would feel „safer‟ that payments would actually occur (public utilities often fall into this category). What is the present value of the bond?
Assume a 6.0% discount rate.
PV (1+ i%)n = FV PV (1.06)8 = $14,000,000 PV = $8,783,773
The $14 Million, 4-year Zero-Coupon Bond
• Present Value: • $6,773,530 if the discount rate is 9.5% • $8,783,773 if the discount rate is 6.0% • The PV being worth „less‟ at a higher discount rate is not terribly intuitive… you might think in terms of how much money you must put into a bank & draw interest in order to hit a $14 million goal. If the interest rate is high, you don‟t need to put as much in the bank.
What if we had a series of future cash inflows or outflows?
• For example, you make a $5,000 investment to buy a machine that will provide $1,000 worth of cash inflow for the next 10 years. Assume the discount rate is 16%.
• What is the present value of the machine?
Annuities
If you have a steady stream of cash inflows, you can do a bunch of PV calculations (and keep changing “n”), or you can use the present value of an annuity formula:
PVA = (payment /i) [1 - 1 / (1+ i)n]
The Generic Machine
PVA = ($1,000 /16%) [1 - 1 / (1+ 16%)10] = $4,833.20 HEY…That‟s a pretty wicked formula! Alternatively, we can use PVA tables (distribute) PVA = 4.8332 $1,000 = $4,833.20
NOT Intuitive
$22,000 × 3.6048 = $79,305.6 minus $75,000 = “b”
Exam Example
• An investment opportunity costing $75,000 is expected to yield net cash flows of $22,000 annually for five years. The NPV of the investment at a discount rate of 12% would be: • a. $ (4,306) i = 10% i = 12% • b. $ 4,306 • c. $75,000 n=4 3.1699 3.0373 • d. $79,306 • e. None of the above
n=5
3.7908
3.6048
Reality vs. the Exam
• In the real world, people perform present value calculations using Excel or financial calculators. Rarely does anyone consult the present value tables. • For the exam, we don‟t have access to Excel; therefore, homework & test questions use the PV tables.
Reality vs. the Exam
• In my opinion, the present value tables make the problems easier relative to financial calculators because it‟s harder to make a mistake.
• Future accounting and finance courses join reality by using Excel.
More Practice
The winner of the Texas lottery “wins $20 million.” If $1 million is received each year for 20 years, what is the “value” of the lottery win?
Assuming a 7% discount rate & the first payment is made at the end of year 1:
PVA = (payment /i) [1 - 1 / (1+ i)n] = $10.6 million
More Practice
The winner of the Texas lottery “wins $20 million.” If $1 million is received each year for 20 years, what is the “value” of the lottery win?
Assuming a 7% discount rate & the first payment is made at the end of year 1:
PVA factor n 20, i 7% = 10.5940 factor × $1 million = $10.6 million
Net Present Value Problems – The Simple Decision Rule
If NPV > 0, you should engage in the project.
If NPV < 0, you should decline the project.
Remaining Methods Consider the Time Value of Money…this is the finance intro.
1. Net Present Value 2. Internal Rate of Return
Internal Rate of Return (IRR)
• PV (1+ i)n = FV • PV, FV, and n are “known”…solve for i • Compare the “internal rate of return” to the discount rate (think “borrowing rate”)…the decision rule is:
– accept project if borrowing rate < IRR – reject project if borrowing rate > IRR
Solving IRR Problems
• Using formulas to solve IRR problems is difficult if we have an annuity. It‟s not bad if we have a simple present value.
• You can use the PVA tables to solve such problems using a “trial and error” approach. • Again, in the real world, Excel & financial calculators solve these problems.
A single cash payment is solvable
Z company mines silver. They are considering purchasing a new mine for $7 million. If they buy the mine, they expect a net $11 million cash inflow in 5 years (when they extract the silver). The company has an 10% discount rate. Calculate the project‟s IRR. PV (1+ i%)n = FV $7 M (1+ i%)5 = $11 M You need to take the 5th 5 = 1.5714 (1+ i%) root of 1.5714 here… IRR = 9.46%
Trial and Error Approach
• • • • $7M (1+ i)n = $11M (1+ i)n must be bigger than one These are called future value numbers. Our text tables report present value numbers…these are equal to 1 divided by the future value numbers…these numbers are smaller than one.
Trial and Error Approach
• $11 M × some number = $7 M • “some number” = .63636363636363636363 • Looking at page 450, “some number” must be on the n = 5 row (this is a 5-year project). • What we know from the table: the number is between 9% and 10%.
Decision Rule
– accept project if borrowing rate < IRR – reject project if borrowing rate > IRR
10% discount rate, 9.5% IRR REJECT
IRR - Annuities
This type of statement can cause confusion
Blue Company can buy a machine for $11 million. If they buy the machine, they will receive $1 million in cash inflow for each of the next 20 years. The company has a 7% discount rate. Calculate the IRR of this project.
Solving for “i” in the formula is very difficult.
PVA = (payment /i) [1 - 1 / (1+ i)n]
IRR – Trial and Error
PVA = Annual Payment (PVA factor from table) $11 M = $1 M (PVA factor from table)
11 = PVA factor from table
we know N = 20
i = 6% N = 20 11.4699
i = 7% 10.5940
i = 8% 9.8181
Decision Rule
– accept project if borrowing rate < IRR – reject project if borrowing rate > IRR
7% discount rate, 6.5% IRR REJECT