Question

A new manufacturing plant costs $5,500,000 to build. Operating and maintenance costs are estimated to be $41,000 per year, and a salvage value of 25% of the initial cost is expected. The units the plant produces are sold for $40 each. Sales and production are designed to run 365 days per year. The planning horizon is 10 years. Find the break-even value for the number of units sold per day for each of the following values of MARR: 5% 10% 15%. Carry all interim calculations to 5 decimal places and then round your final answer up to the nearest unit.

Answer 1

1) At break even Total cash inflow =Total cash outflow .

Present value of operating cost =PVAF@5%,10 * Cost

= 7.72173 * 41000

= 316591.1321 (Cash outflow)

Present value of salvage value = PVF@5%,10 * Salvage

= .61391* (5,500,000* .25)

= 844126.25( cash inflow)

Present value of total Revenue need to break even = 5,500,000+ 316591.1321 - 844126.25 = $4972464.882

Number of units needed = (Total revenue /PVAF@5%,10) / (365 * Rate )

= (4972464.882 / 7.72173) / (365 *40)

= 643957.3622 / 14600

= 44.1067 units per day [rounded to 44 ]

2)

At break even Total cash inflow =Total cash outflow .

Present value of operating cost =PVAF@10%,10 * Cost

= 6.14457 * 41000

= 251927.37 (Cash outflow)

Present value of salvage value = PVF@10%,10 * Salvage

= .38554* (5,500,000* .25)

= 530117.5 ( cash inflow)

Present value of total Revenue need to break even = 5,500,000+ 251927.37-530117.5

= 5221809.87

Number of units needed = (Total revenue /PVAF@10%,10) / (365 * Rate )

= (5221809.87 / 6.14457) / (365 *40)

=849825.109 / 14600

= 58.207 units per day [rounded to 58 ]

3)

At break even Total cash inflow =Total cash outflow .

Present value of operating cost =PVAF@15%,10 * Cost

= 5.01877 * 41000

= 205769.57 (Cash outflow)

Present value of salvage value = PVF@15%,10 * Salvage

= .24718* (5,500,000* .25)

= 339872.5( cash inflow)

Present value of total Revenue need to break even = 5,500,000+ 205769.57 -339872.5

= 5365897.07

Number of units needed = (Total revenue /PVAF@15%,10) / (365 * Rate )

= (5365897.07/ 5.01877) / (365 *37)

= 1069165.766/ 14600

= 73.2305 units per day [rounded to 73 ]