(a)
The monthly leasing cost for 1 apartment.
Answer to Problem 77P
The monthly leasing cost for 1 apartment is $58853.13.
Explanation of Solution
Given:
The cost of land is $3.2 M.
The cost of building is $4.8 M.
The annual operating and maintenance cost is $850000.
The annual property tax and insurance is 6% of initial value of building.
The vacancy rate is 12% of initial value of building.
The owner wants
Concept used:
Write the expression for initial value of building.
VI=CL+CB ...... (I)
Here, the initial value of building is V1, cost of land is CL and cost of building is CB.
Write the expression for salvage value at the end of 20 years.
S=CL+(40%×CB) ...... (II)
Here, the salvage value is S.
Write the expression for annual expenses.
E=COM+P ...... (III)
Here, operating cost is COM and property tax and insurance is P.
Write the expression for principle.
P=Annual investment+E ...... (IV)
Write the expression to calculate monthly leasing total amount.
V1=(A−P)[(1+i)n−1i(1+i)n]+S[1(1+i)n] ...... (V)
Here, monthly leasing total amount is A.
Write the expression for monthly leasing cost for 1 apartment.
M=AN ...... (VI)
Here number of rented apartment is N.
Calculations:
Calculate the initial value of building.
Substitute $3.2 M for CL and $4.8 M for CB in Equation (I).
VI=$3.2 M+$4.8 M=$8 M=$8000000
Calculate salvage value at the end of 35 years.
Substitute $3.2 M for CL and $4.8 M for CB in Equation (II).
S=$3.2 M+(10100×$4.8 M)=$3.2 M+$0.48 M=$3.68 M=$3680000
Calculate the annual investment.
Annual investment=($8 M−$3.68 M)35=$4.32 M35=$123428.57
Calculate annual expenses.
Substitute $850000 for COM and 6%×$8 M for P in Equation (III).
E=$850000+(6%×$8 M)=$850000+$480000=$1330000
Calculate the principle.
Substitute $1330000 for E and $123428.57 for annual investment in Equation (IV).
P=$123428.57+$1330000=$1453428.57
Calculate the total amount for leasing 30 units.
Substitute $1453428.57 for P, $8000000 for VI, $3680000 for S, 0.1512=0.0125 for i and 12×35=420 for n in Equation (V).
$8000000=[(A−$1453428.57)[(1+0.0125)420−10.0125(1+0.0125)420]+$3680000[1(1+0.0125)420]]$8000000=(A−$1453428.57)(79.5663)+$3680000(0.0054)$8000000=A(79.5663)−$115643933.6+$19949.61A=$1553722.67
Calculate monthly leasing cost for 1 apartment.
Substitute $1553722.67 for A and 88%×30 for N in Equation (VI).
Monthly cost=$1553722.6788%×30=$1553722.6726.4=$58853.13
The monthly leasing cost for 1 apartment is $58853.13.
Conclusion:
The monthly leasing cost for 1 apartment is $58853.13.
(b)
If combining 2 units into exercise facility is a good decision or not.
Answer to Problem 77P
Combining 2 units into exercise facility does not seem to be a good decision as it fetches less per-unit lease rentals.
Explanation of Solution
Given:
2 units are turned into exercise facility and the vacancy rate is reduced by 5%.
By turning 2 units into exercise facility total available apartments are 28.
The vacancy rate is reduced by 5% so occupancy rate is 95%.
Calculate monthly leasing cost for 1 apartment.
Substitute $1553722.67 for A and 95%×28 for N in Equation (VI).
Monthly cost=$1553722.6795%×28=$1553722.6726.6=$58410.63
The monthly leasing cost for 1 apartment by turning 2 units into exercise facility is $58410.63.
Combining 2 units into exercise facility does not seem to be a good decision as it fetches less per-unit lease rentals.
Conclusion:
The monthly leasing cost for 1 apartment by turning 2 units into exercise facility is $58410.63.
Combining 2 units into exercise facility does not seem to be a good decision as it fetches less per-unit lease rentals.
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Chapter 6 Solutions
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