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1. Assume you are told that by investing $100,000 now, you will receive $10,000

ID: 2561167 • Letter: 1

Question

1. Assume you are told that by investing $100,000 now, you will receive $10,000 per year starting in year 5 and continuing forever. If you accept the offer, the rate of return on the investment is:

A. Less than 10% per year

B. 0% per year

C. 10% per year

D. Over 10% per year

Formula used:

2. If you invest $5,123 in a venture now, and will receive $1,110 per year for the next 20 years; assuming 10% interest, what is the discounted payback period for your investment?

A. 9 years

B. 8 years

C. 7 years

D. 6 years

E. 5 years

Formula used:

3. An environmental testing company needs to purchase 40,000 worth of equipment 2 years from now. At an interest rate of 20% per year, compounded pounded quarterly, the present worth of the equipment is closest to:

A. $27,070

B. $27,800

C. $26,450

D. $28,220

Formula used:

4. A steel fabrication company invested 800.000 in a new shearing unit. At an annual interest rate of 12%, compounded monthly, the monthly income required to recover the investment in 3 years is approximately:

A. $221,930

B. $31,240

C. $29,160

D. $26,570

Formula used:

5. If compounding is monthly, find the nominal interest rate that will a 43,000 single payment at the end of 4 years equivalent to a 2,000 quarterly payment make over 4 years.

A. 16.08%

B. 16.40%

C. 15.00%

D. 15.50%

Formula used:

Explanation / Answer

Answer to 1

c) 10% per year

Rate of return = Annual payment / Perpetuity price X 100 [Since interest is continuing forever]

= 10000/ 100000 X 100 = 10%

Answer to 2

b) 8 years

Formula = A + (B/C)

A - Last period with a negative discounted cumulative cash flow

B - Absolute value of discounted cumulative cash flow at the end of the period A

C - Discounted cash flow during the period after A

Calculation

Initial investment = 5123

Years (n) = 20

Rate (i) = 10%

CF = 1110

Last period with a negative discounted cumulative cash flow (A) = 6

Absolute value of discounted cumulative cash flow at the end of the period (B) = 289

Discounted cash flow during the period after (C) = 165

Discounted Payback Period = A + (B / C) = 6 + (289 / 165) = 7.75 years = 8 years (rounded off)

Answer to 3

A. $27070

Formula: PV = FV / [1+R]^n

Where

PV = Present value

FV = Future value

R = Effective interest rate

n = Number of years

Computation

Present value = 40000 / [1+22%]^2

= 27073.57

Calculation of effective interest rate

Effective interest rate = (1+i/n)^n - 1

Where i = normal interest rate

n = number of compunding periods

= (1+20%/4)^4 - 1 = 22%

Year(n) Cash flow (CF) Present value=1/(1+i)^n Discounted cash flow (CF X PV) Cumulative Discounted cash flow (CCF) 0 -5123 1 -5123 -5123 1 1110 0.909 1009 -4114 2 1110 0.826 917 -3197 3 1110 0.751 834 -2363 4 1110 0.683 758 -1604 5 1110 0.621 689 -915 6 1110 0.564 627 -289 7 1110 0.513 570 281 8 1110 0.467 518 799 9 1110 0.424 471 1270 10 1110 0.386 428 1697 11 1110 0.350 389 2087 12 1110 0.319 354 2440 13 1110 0.290 322 2762 14 1110 0.263 292 3054 15 1110 0.239 266 3320 16 1110 0.218 242 3561 17 1110 0.198 220 3781 18 1110 0.180 200 3981 19 1110 0.164 181 4162 20 1110 0.149 165 4327