Question

PART 1:

Find the present value for the following income stream if the interest rate is 7% percent and the payments occur at the end of each year. Cash flow for years 1-4: $750, years 5-11: $800, years 12-17: $1,100

A. $4,767

B. $8,321

C. $6,328

D. $5,189

PART 2:

How long will it take a sum of money to double in value if the annual interest rate is 10 percent? Round answer to one decimal.

A. 20.0 years
B. 7.3 years
C. 12.6 years
D. Insufficient information to determine – we need to know the amount of the initial investment

Answer 1

Part I:-

We will determine the Present Value using the PV Factors

For instance,

PV Factor for Year 1 = 1 / (1+7%) ^ 1 = 0.9345

PV Factor for Year 2 = 1 / (1+7%) ^ 2 = 0.8734

And so on..

Attaching the excel sheet with 2 images, one showing final value obtained and second showing formulas used:-

A. В C. E F 1 Years Cash Flows PV Factors Present Value of Cash Flows Discount Rate 7% 1 750 0.93458 700.9346 4 2 750 0.87344 655.0790 5 3 750 0.81630 612.2234 0.76290 6 750 572.1714 7 5 800 0.71299 570.3889 б 800 0.66634 533.0738 7 800 0.62275 498.1998 0.58201 465.6073 10 8 800 11 800 0.54393 435.1470 12 10 800 0.50835 406.6794 13 11 800 0.47509 380.0742 14 12 1100 0.44401 488.4132 15 13 1100 0.41496 456.4609 16 14 1100 0.38782 426.5990 17 15 1100 0.36245 398.6906 372.6081 18 16 1100 0.33873 1100 19 17 0.31657 348.2318 Sum 20 8320.5824 LO 0o an st co

A C E F 1 Present Value of Cash Flows Years Cash Flows Discount Rate 2 PV Factors | =1/(1+$F$3)^B3 =1/(1+$F$3)^B4 -1/(1+SF$3)^B5 1/(1+$F$3)^B6 -1/(1+$F$3)^B7 =1/(1+$F$3)^B8 1/(1+$F$3)^B9 -1/(1+$F$3)^B10 1/(1+$F$3)^B11 1/(1+$F$3)^B12 1/(1+$F$3)^B13 1/(1+$F$3)^B14 1/(1+$F$3)^B15 -1/(1+$F$3)^B16 1/(1+$F$3)^B17 1/(1+$F$3)^B18 -1/(1+SF$3)^B19 -С3*D3 750 0.07 C4*D4 4 2 750 -С5*D5 5 750 C6*D6 6 4 750 C7*D7 7 5 800 -C8*D8 б 800 C9*D9 7 800 C10*D10 10 800 C11*D11 11 800 C12*D12 12. 10 800 C13*D13 13 11 800 C14*D14 14 12. 1100 C15*D15 15 13 1100 1100 C16* D16 16 14 C17*D17 17 15 1100 1100 C18*D18 18 16 C19*D19 19 17 1100 Sum -SUM(E3:E19) 20 st LO st

Hence, PV of Income Stream = $ 8,321 (Option B)

Part II :-

We will use the Excel function "NPER" to determine the number of years required to double the investment.

NPER function has the following syntax:-

NPER (Interest Rate, PMT, PV, FV)

Interest Rate = Annual Interest Rate of 10% in this problem

PMT = 0 (Since, no investment is required to be made yearly)

PV = Initial Investment made ( Let us assume that to be $100)

FV = 2*100 = $200

Attaching the excel snapshots :-

22 -100 23 PV 24 FV 200 10% 25 Interest Rate 26 NPER 7.2725409 27

23 PV -100 24 FV 200 25 Interest Rate 0.1 | =NPER(D25,0,D23,D24) 26 NPER 27

Hence, required no of years = 7.3 years (Option B)