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Click here to read the eBook: Net Present Value (NPV) Click here to read the eBook: Internal Rate of Return (IRR) NPV AND IRR A store has 5 years remaining on its lease in a mall the property in a year and wants rent at that time to be high so that the property will appear more valuable. Therefore, the store has been offered a "great deal" (owners words) on a new 5-year lease. The new lease calls for no rent for 9 months, then payments of $2,600 per month for the next 51 months. The lease cannot be broken, and the store's WACC is 12% (or 1% per month). . Rent is $2,000 per month, 60 payments remain, and the next payment is due in 1 month. The malr's owner plans to sel Should the new lease be accepted? (Hint: Be sure to use 1% per month.) b. If the store owner decided to bargain with the mali's owner over the new lease payment, what new lease payment would make the store owner indifferent between the and old leases? (Hint: Find FV of the old lease's original cost at t 9; then treat this as the PV of a 51-period annuity whose payments represent the rent during months 10 to 60.) Round your answer to the nearest cent. Do not round your intermediate calculations two leases? (Mint: wAcc-it could be higher or lower. At what nominal WACC would the store owner be indifferent between the places. Do nor Calculate the differences between the two payment streams; then find its IRR.) Round your answer to two decimal

Explanation / Answer

NPV of the old lease = 2000/(1+1%)^1 + 2000/(1+1%)^2+ 2000/(1+1%)^3 +……………..+2000/(1+1%)^60

This is a geometric series with first term = 2000/(1+1%) and common ratio =1/(1+1%) = 1/1.01 and number of terms = 60

Sum of geometric series = First term * (1- (common ratio^n))/(1-common ratio)

NPV of the old lease = 2000/(1+1%) *(1- (1/1.01)^60)/(1-(1/1.01))

                                              =$89910.08

NPV of the new lease = 2600/(1+1%)^10 + 2600/(1+1%)^11+ 2600/(1+1%)^12+………..+2600/(1+1%)^60

This is a geometric series with first term = 2600/(1+1%)^10 and common ratio =1/(1+1%) = 1/1.01 and number of terms = 51

Sum of geometric series = First term * (1- (common ratio^n))/(1-common ratio)

NPV of the new lease = 2600/(1+1%)^10 *(1- (1/1.01)^51)/(1-(1/1.01))

                                              =$94611.45

As the NPV of new lease is higher, store owner will have to still pay more than old lease even if first 9 months are free. It should not be accepted.

The rent in the new lease should be such that the NPV remains the same as the old lease.

Therefore, let’s assume rent to be X and equate the NPV of the new lease to $89910.08

NPV of the new lease = X/(1+1%)^10 + X/(1+1%)^11+ X/(1+1%)^12+………..+X/(1+1%)^60 = $89910.08

This is a geometric series with first term = X/(1+1%)^10 and common ratio =1/(1+1%) = 1/1.01 and number of terms = 51

Sum of geometric series = First term * (1- (common ratio^n))/(1-common ratio)

NPV of the new lease = X/(1+1%)^10 *(1- (1/1.01)^51)/(1-(1/1.01)) = $89910.08

    X*36.3890 = $89910.08

  X =$2470.80

Store owner will not mind paying $2470.80 as monthly rent

Store owner would be indifferent to two leases at crossover rate which is the rate at which both the NPVs are equal their rents remaining 2000 for old lease and 2600 for new lease. The rate has to be calculated in this part of the question.

Let the WACC / crossover rate be written as i in the equations

Equating NPV of old lease with NPV of new lease, we get

2000/(1+i%)^1 + 2000/(1+i%)^2+ 2000/(1+i%)^3 +……………..+2000/(1+i%)^60 = 2600/(1+i%)^10 + 2600/(1+i%)^11+ 2600/(1+i%)^12+………..+2600/(1+i%)^60

Now get difference of rents for each months and use excel function ‘=IRR(cashflows)’ to get I =0.01911

If you get error, use =IRR(B1:B60,5%) as sometimes excel needs you to guess what the value would be like

Method without excel – trial and error

2000/(1+i) * (1-(1/(1+i)^60)/ (1-(1/1+i)) = 2600/(1+i)^10 * (1-(1/(1+i)^51)/ (1-(1/(1+i))

2000/(1+i) * (1-(1/(1+i)^60) = 2600/(1+i)^10 * (1-(1/(1+i)^51)

(1-(1/(1+i)^60) = 1.3/(1+i)^9 * (1-(1/(1+i)^51)

(1-(1+i)^-60) = 1.3*(1+i)^-9 * (1-(1+i)^-51)

1.3*(1+i)^-9 * (1-(1+i)^-51) - (1-(1+i)^-60) = 0

Use trial and error to get I= 0.0191

I= 8% , LHS = -0.3526

I=6% LHS = -0.2396

I=4% LHS = -0.1151

I=3% LHS = -0.054

I=2% LHS = -0.0036

i = 0.01911 ~2%

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