The present worth of the first 4 year of after tax cash flow from the barge.

Question

Want to see more full solutions like this?

Answer 1

Question

Chapter 12, Problem 39P

To determine

The present worth of the first $4$ year of after tax cash flow from the barge.

Expert Solution & Answer

Answer to Problem 39P

The present worth of the first $4$ year of after tax cash flow from the barge is $$5815022$ .

Explanation of Solution

Given:

Cost of the barge is $$13.2 million$ .

Expected income from the barge is $$7.5 million$ for the first year.

Growth in income is $$1 million$ per year.

Expenses for the first year is $$2.6 million$ .

Growth in expenses is $$400,000$ per year.

The tax rate is $38%$ .

MARR is $12%$ .

Concept used:

Write the equation for the base book value.

$(Base book value)nth year=[(Book value) ( n−1 ) th year−(( MACRS rate)× ( Book value ) ( n−1 ) th year)]$

Write the formula to calculate the taxable income.

$TI=BTCF−DI$

Here, the taxable income is $TI$ , the depreciation is $DI$ and the before tax cash flow is $BTCF$ .

Write the formula to calculate the taxable amount.

$TAX=0.38×TI$

Here, the taxable amount is $TAX$ .

Write the formula to calculate the after tax cash flow.

$ATCF=TAX+BTCF$

Here, the after tax cash flow is $ATCF$ .

Calculation:

The projected revenue for the first year is $$7,500,000$ .

The revenue of the project is growing $$1,000,000$ for each year.

Calculate the project revenue for second year.

$Revenue2nd=Revenue1st+$1000000=$7500000+$1000000=$8500000$

Calculate the project revenue for third year.

$Revenue3rd=Revenue2nd+$1000000=$8500000+$1000000=$9500000$

Calculate the project revenue for fourth year.

$Revenue4th=Revenue3rd+$1000000=$9500000+$1000000=$10500000$

The operating and maintenance cost for first year is $$2,600,000$ .

The expenses of operating and maintenance cost is increasing by $$400,000$ for each year.

Calculate the operating and maintenance cost for second year.

$(Operating and Maintenance cost)2nd=[( Operating and Maintenance cost) 1 st +$400000]=$2600000+$400000=$3000000$

Calculate the operating and maintenance cost for third year.

$(Operating and Maintenance cost)3rd=[( Operating and Maintenance cost) 2 nd +$400000]=$3000000+$400000=$3400000$

Calculate the operating and maintenance cost for fourth year.

$(Operating and Maintenance cost)4th=[( Operating and Maintenance cost) 3 rd +$400000]=$3400000+$400000=$3800000$

Calculate the net revenue as shown in table below.

Year	Projected revenue (a)	Operating and maintenance cost (b)	Net revenue $(a−b)$
$1$	$$7500000$	$$2600000$	$$4900000$
$2$	$$8500000$	$$3000000$	$$5500000$
$3$	$$9500000$	$$3400000$	$$6100000$
$4$	$$10500000$	$$3800000$	$$6700000$

Calculate the book value by using MACRS percentage rate as shown in table below.

Year	MACR rate (a)	Base book value (b)	Depreciation charge $(a×b)$	Net book value $b−(a×b)$
$1$	$10%$	$$13200000$	$$1320000$	$$11880000$
$2$	$18%$	$$11880000$	$$2138400$	$$9741600$
$3$	$14.40%$	$$9741600$	$$1402790.4$	$$8338809.6$
$4$	$11.52$	$$8338809.6$	$$960630.9$	$$7378178.7$

Calculate the gain on the salvage value as shown below.

$Gain=(Expected salvage value−Net book value after 3 year)$

Substitute $$0$ for expected salvage value and $$7378178.7$ for net book value.

$Gain=($0−$7378178.7)=−$7378178.7$

Calculate the tax effect as shown below.

$Tax effect=Gain×Tax rate$

Substitute $−$7378178.7$ for Gain and $38%$ for Tax rate.

$Tax effect=−$7378178.7×0.38=−$2803707.9$

Calculate the net salvage value after fourth year as shown below.

$Net salvage value=Expected salvage value−Tax effect$

Substitute $$0$ for expected salvage value and $−$2803707.9$ for tax effect.

$Net salvage value=$0−(−$2803707.9)=$2803707.9$

Take before tax cash flow for the first year is $$4900000$ .

Calculate the taxable income for the first year.

$Taxable income= Before tax cash flow− depreciation$

Substitute $$4900000$ for before tax cash flow and $$1320000$ for depreciation.

$Taxable income= $4900000−$1320000=$3580000$

Calculate income tax for first year as shown below.

$Income tax=38% of taxable income$

Substitute $$3580000$ for taxable income.

$Income tax=0.38×$3580000=$1360400$

Calculate the after tax cash flow for the first year as shown below.

$After tax cash flow=Before tax cash flow+Income tax$

Substitute $$4900000$ for before tax cash flow and $$1360400$ for income tax.

$After tax cash flow=$4900000+$1360400=$6260400$

Calculate the after tax cash flow as shown in table below for all the subsequent years.

Year	BTCF	Depreciation	Taxable income	Income tax	ATCF
$0$	$−$13200000$				$−$13200000$
$1$	$$4900000$	$$1320000$	$$3580000$	$$1360400$	$$6260400$
$2$	$$5500000$	$$2138400$	$$3361600$	$$1277408$	$$6777408$
$3$	$$6100000$	$$1402790.4$	$$4697210$	$$1784939.65$	$$7884939.65$
$4$	$$6700000$	$$960630.9$	$$5739369$	$$2180960.26$	$$8880960.26$

Write the equation for present worth factor of annuity (PW).

$PW=D+A(PA, i, n)+F(PF, i, n)=D+A( ( 1+i ) n−1i ( 1+i ) n)+F(1 ( 1+i ) n)$

Here, the present worth is PW, initial payment is D, present value of money is P, interest rate is i, the after tax cash flow is A, the net salvage amount is F, and the number of year is n.

Substitute $−$13200000$ for D, $$6260400$ for A, $12%$ for i, $4 years$ for n and $$0$ for F.

$PW=(−$13200000+$6260400( ( 1+0.12 ) 4 −1 0.12 ( 1+0.12 ) 4 )+$0( 1 ( 1+0.12 ) 4 ))=(−$13200000+$6260400(3.037))=(−$13200000+$19015022)=$5815022$ .

Conclusion:

Therefore, the present worth of the first $4$ year of after tax cash flow is, $$5815022$ .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

Exercise 5Consider the demand and supply functions for the notebooks market.QD=10,000−100pQS=900pa. Make a table with the corresponding supply and demand schedule.b. Draw the corresponding graph.c. Is it possible to find the price and quantity of equilibrium with the graph method? d. Find the price and quantity of equilibrium by solving the system of equations.

1. Consider the market supply curve which passes through the intercept and from which the marketequilibrium data is known, this is, the price and quantity of equilibrium PE=50 and QE=2000.a. Considering those two points, find the equation of the supply. b. Draw a graph for this equation. 2. Considering the previous supply line, determine if the following demand function corresponds to themarket demand equilibrium stated above. QD=.3000-2p.

Supply and demand functions show different relationship between the price and quantities suppliedand demanded. Explain the reason for that relation and provide one reference with your answer.

Answer 2