L1- Value Flashcards
Define Discount Rate
The discount rate is the interest rate used to convert future cash flows into an equivalent one-off upfront sum or present value
Formula for PV with one CF
PV= CF/1.DR^years
Formula for PV with 2 CF in 2 different years
CF1/1.DR^year1 + CF2/1.DR^year2
What are discounted cash flows?
Values that reflect the present worth of future cash flows using a discount rate
Discounted cash flows account for the time value of money.
What is a market based discount rate?
A discount rate that reflects the risk associated with the cash flows in the market context
This concept will be further discussed in relation to risk.
Calculate the present value (PV) of a cash flow of 100 in year 4 with a 7% discount rate.
76.3
PV = 100 / (1.07^4)
What is the present value of receiving a cash flow of 40 in year 2 and 200 in year 10 with a 6% discount rate?
147.3
PV = 40 / (1.06^2) + 200 / (1.06^10)
Fill in the blank: The formula for calculating present value is _______.
[Cash Flow] / (1 + [Discount Rate])^[Number of Years]
True or False: A higher discount rate results in a higher present value.
False
A higher discount rate decreases the present value of future cash flows.
What does NPV stand for?
Net Present Value
How is NPV calculated?
NPV = PV − I, I=the cost of acquiring the cash flow (I), PV= PV of a CF
What does I represent in the NPV formula?
Cost of acquiring the cash flow
If an investment of 150 yields a cash flow of 40 in year 2 and 200 in year 10, what is the discount rate used in the example?
6%
Calculate the NPV using the cash flows of 40 in year 2 and 200 in year 10 with an investment of 150 and a 6% discount rate.
−2.7
True or False: A negative NPV indicates that you are better off making the investment.
False
What conclusion can be drawn from a negative NPV?
You are better off not investing.
What is the optimal criterion for investment decision?
Maximise the net present value of your investments.
What does Fisher separation imply about shareholders?
All shareholders are better off by maximising the net present value.
What type of discount rate is used in Fisher separation?
Market based discount rate.
What is a perpetuity?
A constant annual cash flow that continues indefinitely
Perpetuities are often used in financial contexts to calculate the present value of cash flows.
Fill in the blank: The present value of a perpetuity can be calculated using the formula PV = Cash Flow / _______.
Discount Rate
True or False: A perpetuity has a fixed cash flow that lasts for a limited period.
False
A perpetuity lasts indefinitely, not for a limited period.
What is the formula used to calculate the present value of a perpetuity?
PV = Cash Flow / Discount Rate
If the annual cash flow is 80 and the discount rate is 4%, how is the present value expressed mathematically?
PV = 80 / 0.04 = 2000
What is a perpetuity with growth?
An annual cash flow that grows by a constant growth rate each year and continues indefinitely.
If the discount rate is 6% and the annual growth rate is 2%, what is the formula for the present value of a perpetuity with growth?
PV = 80 / (0.06 - 0.02) = 2000
Fill in the blank: A perpetuity with growth continues _______.
indefinitely
True or False: In a perpetuity with growth, the cash flow does not change over time.
False
What is the significance of the difference between the discount rate and the growth rate in calculating present value?
It determines the sustainability of the growth in cash flows.
List two key components needed to calculate the present value of a perpetuity with growth.
- Discount rate
- Growth rate
Perpetuity with growth formula
CF/(DR–Growth Rate)
What is an annuity?
A constant annual cash flow that continues until a given period.
If the discount rate is 7% and you receive 100 annually for 10 years, what is the present value formula?
PV = (100/0.07) * [1-(1/1.07^10)] = 702.4
Fill in the blank: The present value of an annuity can be calculated using the formula PV = C * _______ , where C is the cash flow and r is the discount rate.
CF/DR * [1 - (1/(1+DR)^n)]
True or False: An annuity can vary in the amount received each year.
False
What is Annuity with Growth
An annuity with growth is an annual cash flow that grows by a constant growth rate each year and continues until a given period.
How does the cash flow change in an annuity with growth?
The cash flow increases by a constant growth rate each year
What is the formula for calculating the present value (PV) of an annuity with growth?
PV= CF/DR-Growth * [1-(1+Growth/1+DR)^n]
If the discount rate is 9%, the growth rate is 2%, the first cash flow is 100, and the final payment is in year 10, what is the PV?
PV= 100/0.09-0.02 * [1-(1.02/1.09)^10]
=693
What does a standard bond contract consist of
–Face Value
–Coupon Interest payment (as % of face value)
What happens when a bond matures?
The bondholder receives the face value of the bond along with the final interest payment.
Define Face Value
The principal amount
How is the present value (PV) of a bond calculated?
PV couponpayments + PVfacevalueatmaturity
OR
PV (annuity of coupon payments) + (PV final payment of principal)
What is the formula for calculating the present value of the coupon payments?
(Face Value * Coupon Interest)/DR * [1-(1/1.DR^n] + Face value/1.DR^n
Calculate the present value of a 10-year bond with a face value of 100, a 5% coupon rate, and a market discount rate of 6%.
100(0.05)/0.06 * (1-1/1.06^10) + 100/1.06^10
92.64
What is the present value of the face value repaid at maturity?
Face Value/ (1+DR)^n
How is the value of a stock determined?
The value of a stock is the discounted value of all future dividend payments
What assumptions are made to calculate the value of a stock using the perpetuity with growth formula?
–Growth rate of dividends (constant over time).
–First year’s dividend amount.
–Market-based discount rate
What formula is used to calculate the value of a stock with growing dividends?
Dividend/(DR-growth of dividends)
Calculate the value of a stock that pays a dividend of 11 next year, has a growth rate of 1%, and a discount rate of 12%.
11/(0.12-0.01) = 100
Why does the perpetuity with growth formula work for valuing stocks?
It assumes dividends grow at a constant rate indefinitely, making it a good fit for long-term stock valuation.
How can the value of a business be determined?
PV Method
What is the formula for calculating the present value (PV) of future cash flows?
CF1/(1+r)^1 + CF2/(1+r)^2 +…+ CFn/(1+r)^n
How do you calculate the value of a business with cash flows for different years and a market share in year 7?
i=1
∑ CFi/(1+r)^1 + (Market Share * Industry
Value) / (1+r)^7
7
For a business with cash flows of 5m in year 1, 5.5m in year 2, and 6m from year 3 to year 7, and a market share of 2% in year 7, how is the present value calculated?
5/1.1 + 5.5/1.1^2 + 6/1.1^3 +…+ 6/1.1^7 + (3000 * 0.02)/1.107
What is the significance of the market share and industry value in calculating the value of the business?
The market share helps estimate the portion of the total industry value that the business will contribute in the final year (year 7), and it is discounted to the present.
How can the present value (PV) method be used in operations management?
The PV method can be used to minimize costs by comparing the total costs of different options over their lifetimes, accounting for both initial and ongoing costs.
When comparing two machines, what factors are important to consider using the PV method?
–Initial cost of the machine.
–Annual maintenance costs over the lifetime of the machine.
–Duration of the machine’s life.
–Discount rate to calculate the present value of future costs.
REWRITE ON PAPER AND CONTINUE WITH TECH
What is the payback method in investment decisions?
The payback method is based on counting the number of years it takes for the accumulated cash flow from an investment to cover the initial investment cost.
How is the payback period calculated?
Initial investment/Annual CF
How is the payback period determined for Investment A, which has an annual cash flow of 10 for 30 years and an investment cost of 80?
80/10 = 8 years
How is the payback period determined for Investment B, which has an annual cash flow of 25 for 4 years and an investment cost of 100?
100/25 = 4 years
How should you favour investments with payback
whichever has less payback period
REDO PAYBACK
What is the IRR (Internal Rate of Return) method in investment decisions?
The IRR method calculates the discount rate at which the net present value (NPV) of a project is zero. It helps determine the rate of return the project is expected to generate.
How is the IRR used to make investment decisions?
If IRR > market-based discount rate, the project should be undertaken.
If IRR < market-based discount rate, the project should not be undertaken.
What is a potential problem with the IRR method?
Uniqueness problem—there may be multiple IRRs for a project if cash flows alternate between negative and positive multiple times
Why can’t IRR be used to choose between projects in an either-or situation?
IRR may give conflicting results when comparing mutually exclusive projects. A project with a higher IRR may have a lower NPV, making it less favorable than a project with a lower IRR but higher NPV.
What is the main advantage of the IRR method?
The IRR method provides a straightforward way of evaluating the rate of return for an investment, making it useful for determining whether a project will generate returns that exceed the cost of capital.
