Question

Alice Smith Investors places $50,000 in an investment fund. One year after making the investment, Smith receives $7500 and continues to receive $7500 annually until 10 such amounts are received. Smith receives nothing further until 15 years after the initial investment, at which time $50,000 is received. Assume MARR = 10% and the planning horizon is 15 years.

What is the present worth, internal rate of return, external rate of return?

Please answer all parts of the question, and include a cashflow diagram

Answer 1

	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Initial Investment	$ -50,000.00
Cash received		$ 7,500.00	$ 7,500.00	$ 7,500.00	$ 7,500.00	$ 7,500.00	$ 7,500.00	$ 7,500.00	$ 7,500.00	$ 7,500.00	$ 7,500.00	$              -	$              -	$              -	$              -	$ 50,000.00
Net Cash flow	$ -50,000.00	$ 7,500.00	$ 7,500.00	$ 7,500.00	$ 7,500.00	$ 7,500.00	$ 7,500.00	$ 7,500.00	$ 7,500.00	$ 7,500.00	$ 7,500.00	$              -	$              -	$              -	$              -	$ 50,000.00
MARR	10%
PV of Cash flow	$ -50,000.00	$ 6,818.18	$ 6,198.35	$ 5,634.86	$ 5,122.60	$ 4,656.91	$ 4,233.55	$ 3,848.69	$ 3,498.81	$ 3,180.73	$ 2,891.57	$              -	$              -	$              -	$              -	$ 11,969.60
Net Present Value	$      8,053.86
Internal rate of return, IRR	2.29%
External rate of return	7.05%

Formulas:

	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Initial Investment	-50000
Cash received		7500	7500	7500	7500	7500	7500	7500	7500	7500	7500	0	0	0	0	50000
Net Cash flow	=SUM(B2:B3)	=SUM(C2:C3)	=SUM(D2:D3)	=SUM(E2:E3)	=SUM(F2:F3)	=SUM(G2:G3)	=SUM(H2:H3)	=SUM(I2:I3)	=SUM(J2:J3)	=SUM(K2:K3)	=SUM(L2:L3)	=SUM(M2:M3)	=SUM(N2:N3)	=SUM(O2:O3)	=SUM(P2:P3)	=SUM(Q2:Q3)
MARR	0.1
PV of Cash flow	=B4/(1+$B$6)^B1	=C4/(1+$B$6)^C1	=D4/(1+$B$6)^D1	=E4/(1+$B$6)^E1	=F4/(1+$B$6)^F1	=G4/(1+$B$6)^G1	=H4/(1+$B$6)^H1	=I4/(1+$B$6)^I1	=J4/(1+$B$6)^J1	=K4/(1+$B$6)^K1	=L4/(1+$B$6)^L1	=M4/(1+$B$6)^M1	=N4/(1+$B$6)^N1	=O4/(1+$B$6)^O1	=P4/(1+$B$6)^P1	=Q4/(1+$B$6)^Q1
Net Present Value	=SUM(B7:Q7)
Internal rate of return, IRR	=IRR(B7:Q7,100%)
External rate of return	=MIRR(B7:Q7,B6,B6)