Question

A demonstration of time value using three alternative fact patterns using a $100,000 principal investment over three different time periods and at three different rates. Consider using an annuity under at least one of the fact patterns. (managerial accounting)

Answer 1

Analysis of time value of money
Inputs using for analysis
Investment amount
Case 1
Time period 5 years, amount being repaid in different amounts with Rate of interest (ROI) @12%
Interest is repaid at end of the desired period
Case 2
Time period 10 years, amount being repaid in different amounts with Rate of interest @15%
Interest is repaid alongwith repayments over the desired period
Case 3
Time period 10 years, amount being repaid in annuity amounts with Rate of interest @15%
	Case 1		Case 2		Case 3
ROI	12%		14%		15%
Investment	-100000		-100000		-100000
Years					Annuity	Present value
1	-100000		-100000		17,326	15,066
2					17,326	13,101
3					17,326	11,392
4					17,326	9,906
5	160000				17,326	8,614
6					17,326	7,491
7					17,326	6,514
8					17,326	5,664
9					17,326	4,925
10			240000		17,326	4,283
Prsent value (PV)
Future value	160000		240000			86,957
ROI	12%		14%
Time	5		10
PV	90,788		136,182
Conclusion
case 1	In case of lumpsum repayments the present value seems high
case 2	In case of lumpsum repayments the present value seems higher when repayment gets extended
case 3	In case of annuity since money is being repaid over the period hence the PV is lower