1
SIE/ENGR 265 – HW 4 Solution

1. The annual equivalent amount of the bi-annual payment is

\$11,000 (A/F, 3%, 2) = \$11,000 (0.4926) = \$5,418.60

The capitalized worth is

CW = A = \$5,418 60 = \$180,620
i 0 03

So, \$180,620 must be deposited now into an account earning 3% per year such that \$11,000 can be paid
out every two years indefinitely (starting two years from now).

2. The PW of the incremental investment is:

(8%) = −\$400 + (
15,000

19

15,000

24ℎ
) (
\$3.50

) (/, 8%, 10)

= −\$400 + (164.5 gal/yr) (\$3.50/gal) (6.7101)

= \$3,463

This is a very attractive investment in the Ford truck (\$3,463 > 0).

3. The bond pays (0.05)(\$5,000) = \$250 once per year. The yield, or effective annual interest rate, can be
found as follows:

0 = −\$5,500 + \$250 (P/A, i’%, 10) + \$5,000 (P/F, i’%, 10)

i’% = RATE(NPER,PMT,PV,FV) = RATE(10,250,-5500,5000) = 3.78%

\$5,000

A = \$250 / year

Viewpoint: 0 1 2 3 4 5 6 7 8 9 10
End of year
2
4. P = \$150 (P/A, 2%/qtr., 60 qtr.) + \$10,000 (P/F, 2%/qtr., 60 qtr.)
P = \$150(34.7609) + \$10,000(0.3048)
P = \$5,214 + \$3,048
P = \$8,262

5. FW(15%) = −\$10,000 (F/P,15%,5) + (\$8,000 − \$4000)(F/A,15%,5) − \$1,000

= −\$10,000 (2.0114) + \$4000(6.7424) − \$1,000

= \$5,855.60

Since FW(15%) ≥ 0, the project is acceptable.

6. Let X = annual savings required.

AW(20%) = 0 = X – [\$3,000,000(A/P, 20%, 7) − \$300,000(A/F, 20%, 7)]

X = \$808,980 / year

Net savings per pallet = (\$808,980/year) / (1,000,000 pallets/year) = \$0.81 per pallet

\$255

7.

\$3,000

\$3,000 = \$255 (P/A, i′, 15)

i′ = RATE(NPER,PMT,PV) = RATE(15,255,-3000) = 3.2% per month

r = 12 × 3.2% = 38.4% compounded monthly (APR)
ieff = (1 + ⁄ )

− 1 = (1 +
0.384
12
)
12
– 1 = 0.459 or 45.9% per year

0
1 2 3 14 15
3
\$375

8.

\$350

The CFD is from the lender’s viewpoint. The net cash flow will have a \$350 outflow at end of month 0,
uniform series of inflows of \$25 from at end of months 1-11, and finally a \$375 outflow at end of month
12. Using IRR function, we can then find the interest rate as shown in the table below:

EOM
Net Cash
Flow
0 (\$350)
1 \$25
2 \$25
3 \$25
4 \$25
5 \$25
6 \$25
7 \$25
8 \$25
9 \$25
10 \$25
11 \$25
12 \$375
IRR 7.14%

The monthly interest rate (rmonthly) = 7.14%;
The nominal annual rate (r) = 12 × 7.14% = 85.68%;
The effective annual interest rate is
ieff = (1 + ⁄ )

− 1 = (1 +
0.8568
12
)
12
– 1 = (1.0714)12 – 1 = 1.288 (128.8%).
Jess’s wife is correct in her worry.

0 1 2 3 11 12 