Question

The capital investment for a new highway paving machine is $950000. This expense is estimated, in year zero dollars, is $92600. This expense is estimated to increase at the rate of 5.7% per year. Assume that f=4.5%, N=7 years, MV at the end of the year 7 is 10% of the capital investment, and the MARR (in real terms) is 10.05% per year. What uniform annual revenue (before taxes), in actual dollars, would machine need to generate to break even?

f is the inflation rate

Answer 1

Given cash flows are in nominal (or actual) terms while MARR is in real terms so either convert all cash flows to real or MARR to nominal. We will convert MARR to nominal terms:

MARRnominal = MARRreal + inflation + MARRreal*inflation = 10.05% + 4.5% + (10.05%*4.5%) = 15.00%

For the machine to break even, its NPV should be zero. We can calculate the uniform annual revenue (before taxes) by setting NPV to 0 and solving for revenue, as follows:

Formula	Year (n)	0	1	2	3	4	5	6	7
	Capital investment (CI)	950,000
En-1*(1+5.7%)	Expense (in nominal dollars) En		92,600.00	97,878.20	103,457.26	109,354.32	115,587.52	122,176.01	129,140.04
	Revenue (in nominal dollars) Rn		335,057.18	335,057.18	335,057.18	335,057.18	335,057.18	335,057.18	335,057.18
En - Rn	Net revenue (NR)		242,457.18	237,178.98	231,599.92	225,702.86	219,469.66	212,881.17	205,917.14
1/(1+d)^n	Discount factor @15%		0.870	0.756	0.657	0.572	0.497	0.432	0.376
NR*Discount factor	PV of net revenue (PV)		210,828.20	179,334.37	152,271.77	129,036.24	109,104.54	92,023.60	77,401.28
PV - CI	Total cash flow (CF)	(950,000.00)	210,828.20	179,334.37	152,271.77	129,036.24	109,104.54	92,023.60	77,401.28
Sum of all CFs	NPV	0.00

The machine will break even at a revenue of 335,057.18 per annum.