發(fā)布時間：2016-03-15 09:29

Question1
你想在大學(xué)畢業(yè)三年后到歐洲去拜訪親戚。該行預(yù)計將耗資10000美元，當(dāng)時。你的父母已經(jīng)為你存了5000美元，你在一個支付6%利息，每年三年，從現(xiàn)在開始。希爾達阿姨已經(jīng)同意資助這個平衡。如果你打算把希爾達阿姨的禮物放在三年的投資收入10%，那么她現(xiàn)在要存多少錢，那么你可以在三年后拜訪你的親戚嗎？
由于希爾達阿姨所需的財政平衡，，那么旅行未來支出10000美元應(yīng)同等存款的總和一樣，因為父母存了5000美元在描繪成熟的三年期結(jié)束。
一段時期的結(jié)束是下一個時期的開始，所以
FV（現(xiàn)金流出）= PV（現(xiàn)金流入）；
You want to travel to Europe to visit relatives when you graduate from college three years from now. The trip is expected to cost a total of $10,000 at that time. Your parents have deposited $5,000 for you in a CD paying 6% interest annually, maturing three years from now. Aunt Hilda has agreed to finance the balance. If you are going to put Aunt Hilda’s gift in an investment earning 10% over the next three years, how much must she deposit now, so you can visit your relatives at the end of three years?

Due to Aunt Hilda required finance balance, so the trip future expenditure $10,000 should be the same with equivalent deposit sum, because the parents deposited $5,000 at the end of the period depicted on maturing threes years.
The end of one period is the same as the beginning of the next period, so
FV(cash outflow) =PV(cash inflow);
According to the future value formulation,  , so,
10000美元= 5000元×（1＋6%）3＋1
1 = 4044.92美元
父母的未來價值的沉積需要4044.92美元
未來的價值是一個活期存款將增加一個固定的時間，同時支付復(fù)合利息。當(dāng)提到的問題，我要把阿姨的禮物hilida投資收益10%在接下來的三年，這意味著在我三年的投資回報每年利率將達到10%所以我應(yīng)該知道需求沉積的現(xiàn)值金額。
$10,000 = $5,000*(1+6%)3 +FV1
FV1= $4,044.92
The future value of parents deposition is required to $4,044.92
Future value is the amount to which a current deposit are going to increase over a constant period of time while paying compound interest. As the question mentioned, I am going to put Aunt Hilida’s gift in an investment earning 10% over the next three years, which means in three years my investment annually interest rate of return will arrive at 10% so I should know the amount of the present value of requirement deposition.
Based on the formulation,  
PV= $4,044.92/ (1+10%)3 = $3,039.01
So $ 3,039.01 she should be deposited now that I can visit her at the end of three years.
Question 2
Consider the following two mutually exclusive projects
Year Cash Flow (A) Cash Flow (B)
0 -54,000 -23,000
1 12,700 11,600
2 23,200 11,200
3 27,600 12,500
4 46,500 6,000

The company requires a return of 14% on the investment

A) which project should the company choose based on payback period and why?
When a company budget the capital, payback period is defined to the period of time required to recover the initial expenditure to get the break-even point.(Paul W. et al., 2010) 
Using the formulation to present PB is  
Project A: 3+($54,000-$12,700-$23,200-$27,600/$5,4000)=2.8 years
Project B: 3+($23,000-$11,600-$11,200-$12,500/$23,000)=2.5 years
The method of payback period is the basic aspect of considering whether the investment projects can recover the initial cost. From the result we can see that the project A payback period is 2.8 years while project B is 2.5 years, used less time to recover the initial investment. So based on methods of payback period project B should be selected as the investment item. 

B) Which project should the company choose based on NPV and why?
The net present value is stated as the amount of present values of the individual cash flows of the same entity.(Khan, M.Y., 1993) Moreover, NPV also can be described as the differentiation of discounted sum which mainly pointed out cash inflows and cash outflows. (Grubbström, Robert W., 1967)
The formulation of net present value is  , so

Project A: 
NPV1 = -$54000+ $12,700/(1+14%)1+ $23,200/(1+14%)2+ $27,600/(1+14%)3+ $4,6500/(1+14%)4
  = -$54000+ $11,140.35+ $17,851.65+ $18,629.21+ $27,531.73
  = $21,152.94
Project B: 
NPV2 = -$23,000+ $11,600/(1+14%)1+ $11,200/(1+14%)2+ $12,500/(1+14%)3+ $6,000/(1+14%)4
  = -$23,000+$10,175.44+ $8,618.04+ $8,437.14+ $3,552.48
  = $7,783.1

The calculation process compares the net present value of the difference between project A and B , as well fluctuating inflation and payback.
Both net present value for A and B are positive that certificate that the two types investment of realistic return rate is higher than the required return rate. The investment rate of return for project A is better than the project B thus it can be selected.  
C) Which project should the company choose based on IRR and why?
IRR is internal rate of return is a rate of return applied in capital budgeting to evaluate and confront the profitability of investments. (Hartman, J. C.& Schafrick, I. C., 2004) As for how to run out the internal rate of return, it has closely relationship with net present value, explained by a word a rate of return for which this function is zero is an internal rate of return.
So the function can be described  , the internal rate of return is a rate quantity, hence for project A and B, it is also a emblem of efficiency, effectiveness, or yield of an investment when measure a project. Comparing with the net present value that is an presenter of the magnitude of an investment.
Project A:
IRRa= -$54000+ $12,700/(1+ra)1+ $23,200/(1+ra)2+ $27,600/(1+ra)3+ $4,6500/(1+ra)4 =0
Using excel: ra≈28.50%
Project B:
IRRb=-$23,000+$11,600/(1+rb)1+ $11,200/(1+rb)2+ $12,500/(1+rb)3+ $6,000/(1+rb)4 =0
Using excel: rb ≈30.94%
Both project A and B can be acceptable for the firm because the calculated internal rate of return is higher than their minimum acceptable rate of initial investment. However, in contrast with the initial investment value between projectA and B, A has twice initial capital expenditure than B whereas its internal rate of return is higher than the A.
Hence, only referenced IRR as standards B should be selected due to it using less cost receive more payback. In general, a firm ought to coordinated IRR and NPV or other more complex factors that influence its investment rate of return.
D) Which project should the company choose based on profitability index and why?
Profitability index is the ratio of payoff to investment of a proposed project. It is a useful tool for ranking projects because it allows the  to evaluate the sum of value created per unit of investment.(Audit IT, 2014)
The ratio is calculated as  

Project A:
PVa=$12,700+ $23,200+ $27,600+ $4,6500/(1+14%)4≈ $65,129
PIa= $65,129/$54,000= 1.206
Project B:
PVb= $11,600+ $11,200+ $12,500+ $6,000/(1+14%)4≈ $24,453
PIb= $24,453/$23,000=1.063
Each of project are acceptable because the profitability index higher than 1 separately. But project A perform better than B in making more profit.

E) Which the project the company will final choose and why?
From above calculation, my answer is ‘it’s depends’ for my perspective. But I suggest managers are able to preference consider selecting project A as their investment project. For reason of the result of future payback, net present value, and profitable index, project A acted a obvious advantages than B. Many factors, however, are required managers to be considered when decide a investment project for the real world it ought to be more complex than this questions background. If the investor is small or mid-size company, considered from cash security, the IRR for project A is quite suitable for the small-size cash investment.
Otherwise, may be other factors as policies, currency rate fluctuation, risk assessment and depreciation of machine have great effect on the future investment conducting. 

Reference文獻

Grier C. L., Nagalingam, S. V., 2000. CIM justification and optimization. London: Taylor & Franci. p. 36.

Hartman, J. C.& Schafrick, I. C., 2004. The relevant internal rate of return. The Engineering Economist 49(2), pp 139–158.
Khan, M.Y., 1993. Theory & Problems in Financial Management. Boston: McGraw Hill Higher Education.
Paul W. F., Neil T. Bendle, Phillip E. Pfeifer, David J. Reibstein., 2010. Marketing Metrics: The Definitive Guide to Measuring Marketing Performance. New Jersey: Pearson Education Press.
Grubbström, Robert W., 1967. On the Application of the Laplace Transform to Certain Economic Problems. Management Science (13) pp 558–567. 
Audit IT, 2004. Profitbility Index, 10th September 2014 from Ready Ratios.

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