Question

A city is considering the Base option and the Star option for investment in their public works department for which data is given below. What is the difference between the benefit/cost ratios for the two options?

	BASE OPTION	STAR OPTION
Initial cost	$2,300,000	$3,200,000
Life in years	2	3
Salvage value %	10%	8%
Salvage value $	$230,000	$256,000
Inflation rate p. y.	4%	4%
Other costs 1st year	($150,000)	($575,000)
Increase in other costs p. y.	5%	7%
Benefits in 1st year	$2,500,000	$3,000,000
Increase in benefits p. y.	6%	8%
Interest rate p. y.	5.00%

Group of answer choices

0.11

0.20

0.25

0.28

Answer 1

Answer = 0.20   (see the working notes below)

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Working:

Computation of Benefit Cost Ratio Difference:

                                                                           Base Option    Star Option

                                                                        ------------------                -----------------

Initial Cash outflow    (A)                                    2300000                          3200000

                                                                       --------------------------- ----------------

Present value of net cash inflows:

(annual benefits-costs x discount factor)

Year 1                                                              2150250                          2218875

Year 2                                                              2088715                          2199540

Year 2 (salvage value)                                     192740                            -

Year 3                                                                     -                             2166391

Year 3 (salvage value)                                          -                              196352

                                                                ---------------                    --------------------

Present value of cash inflows     (B)             4431705                      6781158

                                                                   --------------                     -----------------

Benefit Cost Ratio (B/A)                                 1.92                                 2.12

Difference in beneft cost ratio = 0.20

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