What Is Your Understanding of the Following Concepts; Present Value, Present Value of an Annuity, Future Value, and Future Value of an Annuity. (Please Describe Any Formulas Related to Each.)
Present Value is the current worth of a future sum of money or stream of cash flows given a specified rate of return. Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower the present value of the future cash flows. Determining the appropriate discount rate is the key to properly valuing future cash flows, whether they be earnings or obligations.
Present Value of annuity is a series of equal payments or receipts that occur at evenly spaced intervals. Leases and rental payments are examples. The payments or receipts occur at the end of each period for an ordinary annuity while they occur at the beginning of each period; For an annuity due. PVoa = PMT [(1  (1 / (1 + i)n)) / i]
Future Value is the value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today. There are two ways to calculate FV: For an asset with simple annual interest: = Original Investment x (1+ interest rate *number of years)) 2) For an asset with interest compounded annually: = Original Investment x ((1+interest rate)^number of years)
Future value of annuity is the value of a group of payments at a specified date in the future. These payments are known as an annuity, or set of cash flows. The future value of an annuity measures how much you would have in the future given a specified rate of return or discount rate. The future cash flows of the annuity grow at the discount rate and the higher the discount rate, the higher the future value of the annuity.
The current value of a set of cash flows in the future, given a specified rate of return or discount rate.The future cash flows of the annuity are discounted at the discount rate, and the higher the discount rate, the lower the present value of the annuity.
...Presentvalue is where the value on a set date of a future payment is discounted to reflect the time value of money and other factors. This can also apply to a series of future payments. Presentvalue calculations are commonly utilized in business and economics to provide a way to compare cash flows at different times. Presentvalue can be described as the current worth of a future sum of money or stream of cash flows given a specified rate of return. (http://www.getobjects.com) Future cash flows are discounted at the discount rate. The higher the discounted rate, the lower the presentvalue of the future cash flows. Determining what the appropriate discount rate is, is important to correctly place valuefuture cash flows.
The PresentValue of an Ordinary Annuity is the value of a stream of promised or expected future payments that have been discounted to a single equivalent value today. It is extremely useful for comparing two separate cash flows that differ in some way.
PresentValue of an Ordinary Annuity can also be looked at as the amount you have to invest today at a specific interest rate...
.... To find the PVA, we use the equation:
PVA = C({1 – [1/(1 + r)]t } / r )
PVA = $60,000{[1 – (1/1.0825)9 ] / .0825}
PVA = $370,947.84
The presentvalue of the revenue is greater than the cost, so your company can afford the equipment.
7. Here we need to find the FVA. The equation to find the FVA is:
FVA = C{[(1 + r)t – 1] / r}
FVA for 20 years = $3,000[(1.08520 – 1) / .085]
FVA for 20 years = $145,131.04
FVA for 40 years = $3,000[(1.08540 – 1) / .085]
FVA for 40 years = $887,047.61
Notice that doubling the number of periods does not double the FVA.
8. Here we have the FVA, the length of the annuity, and the interest rate. We want to calculate the annuity payment. Using the FVA equation:
FVA = C{[(1 + r)t – 1] / r}
$40,000 = $C[(1.05257 – 1) / .0525]
We can now solve this equation for the annuity payment. Doing so, we get:
C = $40,000 / 8.204106
C = $4,875.55
9. Here we have the PVA, the length of the annuity, and the interest rate. We want to calculate the annuity payment. Using the PVA equation:
PVA = C({1 – [1/(1 + r)]t } / r)
$30,000 = C{[1 – (1/1.09)7 ] / .09}
We can now solve this equation for the annuity payment. Doing so, we get:
C = $30,000 / 5.03295
C = $5,960.72
10. This cash flow is a perpetuity. To find the PV of a perpetuity, we use the equation:
PV...
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Exam 3 Short Essay.
Net Presentvalue is the difference between an investment’s market value and its cost. For an example, you invest 100 dollars (Cost) into a lemonade stand but you receive 50 dollars (Market Value) of cash inflow. Another would be you buy a house for 50,000(Cost) But you sell it for 75,000(Market Value). Your net presentvalue An Investment should be accepted if the net presentvalue is positive and it should be rejected if the net presentvalue is negative. Net presentvalue uses the discounted cash flow of valuation, which is the process of valuing an investment by discounting future cash flows. Comparison to another rule, which is called the Internal rate of return, uses the discount rate that makes the NPV of an Investment zero. IRR finds the single rate that summaries the rate of return of a project. We only depend on cash flow of a particular investment not the rates offered elsewhere. For an example, you let your brother burrow 100 dollars but he pays you back 125 dollars. You would ask what is the return on this investment, which is 25% or 1.25 dollars back for every 1 dollar invested. This investment would be only valid if the required return is less than 25% because anything more would fall in...
...WHY IS THE CONCEPT OF PRESENTVALUE SO IMPORTANT FOR CORPORATE FINANCE?
The importance of concept of presentvalue to the world of corporate finance is that presentvalue calculations are widely used in business and economics to provide a means to compare cash flows at different times. Present Value’s definition and simplistic formula used for normal purchases, the concept’s importance to corporate finance and why presentvalue is the very first topic taught in finance classes explain that presentvalue is an essential knowledgeable tool to ensure we make the best decisions with our money.
However, first, What Does PresentValue  PV Mean? Presentvalue is “the current worth of a future sum of money or stream of cash flows given a specified rate of return. Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower the presentvalue of the future cash flows. Determining the appropriate discount rate is the key to properly valuing future cash flows, whether they are earnings or obligations.” Through the definition itself, an importance to corporate finance is explained as well as why...
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Net presentValue, Mergers and acquisitions
Abstract
Main objective of undertaking this to report was learn about NPV presentvalue (NPV) method to make capital budgeting decision(Google NEW Project) and success factors involved in mergers and acquisitions(GoogleGroupon Case).
Answers to the Assignments
Part I: Google should go ahead with the new project.
PartII: Google’s acquisition of Groupon would have been win win situation for both corporations
Now I will discuss both parts in detail below.
Part I: Capital Budgeting
Capital budgeting is the process of making longterm planning decision relating to planning for capital assets as to whether or not money should be invested in the long term projects (en.wikipedia.com). Decisions like obtaining new facilities or purchase or new machinery to expand their business. It involves a financial analysis of the various alternative proposals regarding a capital expenditure and to select the best out of the several alternatives.
There are several methods of evaluating investment projects like NPV, IRR, Payback period and Profitability Index (www.investopedia.com). I will be discussing NPV and IRR for this assignment.
Net PresentValue (NPV)
NPV is a method which uses discounted cash flow techniques. Net PresentValue is equal to the difference between the Present...
...Chapter 2
How to calculate Presentvalues
Question 6: Perpetuities
An investment costs $1,548 and pays $138 in perpetuity. If the interest rate is 9%, what is the NPV?
Answer
NPV = −1,548 + 138/.09 = −14.67 (cost today plus the presentvalue of the
perpetuity).
Question 7: Growing perpetuities
A common stock will pay a cash dividend of $4 next year. After that, the dividends are expected to increase indefinitely at 4% per year. If the discount rate is 14%, what is the PV of the stream of dividend payments?
Answer
PV = 4/(.14 − .04) = $40.
Question 19: Presentvalues
As winner of a breakfast cereal competition, you can choose one of the following prizes:
a. $100,000 now
b. $180,000 at the end of five years
c. $11,400 a year forever
d. $19,000 for each of 10 years
e. $6,500 next year and increasing thereafter by 5% a year forever.
If the interest rate is 12%, which is the most valuable prize?
Answer
a. PV = $100,000.
b. PV = $180,000/1.125 = $102,136.83.
c. PV = $11,400/0.12 = $95,000.
d.
e. PV = $6,500/(0.12 0.05) = $92,857.14.
Prize (d) is the most valuable because it has the highest presentvalue.
Question 20: Annuities
Siefried Basset is 65 years of age and has a life expectancy of 12 more years. He wishes to invest $20,000...
...
FINC5001 Capital Market and Corporate Finance

Workshop 5 – Capital Budgeting II
1. Basic Concepts Review
a) In applying Net PresentValue, what factors do we include, and what factors do we ignore?
Use cash flows not accounting income
Ignore
* sunk costs
* financing costs
Include
* opportunity costs
* side effects
* working capital
* taxation
* inflation
2. Practice Questions
a) After spending $3 million on research, Better Mousetraps has developed a new trap. The project requires an initial investment in plant and equipment of $6 million. This investment will be depreciated straightline over five years to a value of zero, but, when the project comes to an end in five years, the equipment can in fact be sold for $500,000. The firm believes that working capital at each date must be maintained at 10% of next year's forecasted sales. Production costs are estimated at $1.50 per trap and the traps will be sold for $4 each. (There are no marketing expenses.) Sales forecasts are given in the following table. The firm pays tax at 35% and the required return on the project is 12%. What is the NPV?

Figures in 000's  
Year  0  1  2  3  4  5 
Unit Sales   500  600...
...Part I
A. PresentValue with Discount rate of 7% = 15000/(1+7%) = 15000/1.07 = $14,018.69
PresentValue with Discount rate of 4% = 15000/(1+4%) = 15000/1.04 = $14,423.08
B. Account A  PresentValue with Discount rate of 6% = 6500/(1+6%) = 6500/1.06 = $6,132.08
Account B  PresentValue with Discount rate of 6% = 12600/(1+6%)^2 = 12600/1.1236 = $11,213.96
C.PresentValue of Gold Mine 7% = 4900000/1.07 + 61,000,000/(1.07)^2 + 85,000,000/(1.07)^3
= 45,794,392.52 + 61,000,000/1.1449 + 85,000,000/1.2250
= 45,794,392.52 + 53,279,762.42 + 69,385,319.54
= $168,459,474.48
By using the same concept above we can determine the presentvalue of Gold Mine.
PresentValue of Gold Mine @ 5% = 175,421,660.73
PresentValue of Gold Mine @ 3% = 182,858,207.04
When the discount rate is 7%, the presentvalue of gold mine is $168.46m. This value increase by approximately $6.96 when the discount rate is 2% less than 7%. When the discount rate is 3% value of gold mine is 182.86.
Part II
A. Consider the project with the following expected cash flows:
Year  Cash flow 
0  $400,000 
1  $100,000 
2  $120,000 
3  $850,000 
If the discount rate is 0%,...
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