Question

A savvy business owner who owns several chicken franchises is seeking to add another store to his portfolio of stores. He wants to buy a store in the Memphis market at a cost of $8.00 million. However, the owner will sell the store to him, BUT he also has to buy a second store in the Oxford market at a cost of $6.00 million as part of the deal. The Memphis store is doing well, but the Oxford store has cash flow issues. The business owner will have to buy BOTH stores or NONE at all. The owner has a discount rate of 10.00%. The owner will value the opportunities over a five-year period.

STORE	0	1	2	3	4	5
MEMPHIS	-$8.00	$1.98	$2.10	$2.23	$2.51	$6.00
OXFORD	-$6.00	$0.74	$0.52	$0.84	$0.91	$4.00

What is the NPV and rate of return of buying both stores?

Answer 1

As per the above data, Discount rate is 10%

NPV = R₁/(1+i)¹ + R₂/(1+i)² + R₃/(1+i)³ + .......- Initial Investment

For Memphis:-

NPV

= 1.98/1.1000 + 2.10/1.2100 + 2.23/1.3310 + 2.51/1.4641 + 6.00/1.6105 - 8.00

=1.8000 + 1.7355 + 1.6754 + 1.7144 + 3.7256 - 8.00

=10.6509 - 8.00

=2.6509

For Oxford :-

NPV

=0.74/1.1000 + 0.52/1.2100 + 0.84/1.3310 + 0.91/1.4641 + 4.00/1.6105 - 6.00

=0.6727 + 0.4298 + 0.6311 + 0.6215 + 2.4837 - 6.00

=4.8388 - 6.00

= - 1.1612

Combined NPV = 2.6509 - 1.1612 = 1.4897

IRR (Rate of Return) Calculations:

For Memphis:-

0 = CF₀ + CF₁/ (1+r)¹ + CF₂/ (1+r)² + CF₃/ (1+r)³ + CF4/ (1+r)⁴ + CF5/ (1+r)⁵

​​​​​0 = -8.00 + 1.98 / (1+r)¹ +2.10/ (1+r)² +2.23/ (1+r)³ +2.51/ (1+r)⁴ +6.00/ (1+r)⁵

=20%

For Oxford:-

0 = CF₀ + CF₁/ (1+r)¹ + CF₂/ (1+r)² + CF₃/ (1+r)³ + CF4/ (1+r)⁴ + CF5/ (1+r)⁵

​​​​​0 = -6.00 + 0.74 / (1+r)¹ +0.52/ (1+r)² +0.84/ (1+r)³ +0.91/ (1+r)⁴ +4.00/ (1+r)⁵

=4%

Combined IRR (rate of return) = 20% + 4% = 24%

So, the combined NPV is 1.4897 & Combined IRR (rate of return) is 24%