Question

Los Angeles County Hospital is planning to purchase a new piece of medical equipment with a list price of $3,000,000. The medical equipment supplier presents County with two offers:

Offer 1: County can purchase the medical equipment at a 10% discount off the list price, but it must pay the final (post-discount) price today.

Offer 2: County can purchase the medical equipment at a 5% discount off the list price with two-year, no-cost financing. Under this offer, half of the final (post-discount) price must be paid at the end of year 1, and the remaining half must be paid at the end of year 2.

a. Which offer should County accept if their estimate of the opportunity cost rate is 10%?

b. Which offer should County accept if their updated estimate of the opportunity cost rate is 1%?

Answer 1

Part (a)

Offer (1)

Present value of offer 1 = Post discount price of the equipment

                                      = List price × (1 – Discount rate)

                                      = $3,000,000 × (1 – 0.10)

                                      = $3,000,000 × 0.90

                                      = $2,700,000

Offer (2)

Present value of cash outflows for offer 2 = PV of the first half of the post-discount payment + PV of the second half of the post-discount payment

                                                                   = PV of the first half of the post-discount payment + PV of the second half of the post-discount payment

                                                                   = [First half of the post-discount payment × PVIF_{(r%, n)}]+ [Second half of the post-discount payment × PVIF_{(r%, n)}]

                                                                   = [$1,425,000 × PVIF_{(10%, 1)}]+ [$1,425,000 × PVIF_{(10%, 2)}]

                                                                   = [$1,425,000 × {1 / (1 + r)ⁿ}]+ [$1,425,000 × {1 / (1 + r)ⁿ}]

                                                                   = [$1,425,000 × {1 / (1 + 0.10)¹}]+ [$1,425,000 × {1 / (1 + 0.10)²}]

                                                                   = [$1,425,000 × 0.90909090]+ [$1,425,000 × 0.82644628]

                                                                   = $1,295,454.53 + $1,177,685.95

                                                                   = $2,473,140.48

Working notes-

Post-discount payment = List price × (1 – Discount rate)

                                     = $3,000,000 × (1 – 0.05)

                                     = $3,000,000 × 0.95

                                     = $2,850,000

Half of the post-discount payment = $2,850,000 / 2

                                                        = $1,425,000

Since, present value of cash outflows for offer 2 is less than the offer 1, so offer 2 should be selected.

Part (b)

Offer (1)

Present value of offer 1 = Post discount price of the equipment

                                      = List price × (1 – Discount rate)

                                      = $3,000,000 × (1 – 0.10)

                                      = $3,000,000 × 0.90

                                      = $2,700,000

Offer (2)

Present value of cash outflows for offer 2 = PV of the first half of the post-discount payment + PV of the second half of the post-discount payment

                                                                   = PV of the first half of the post-discount payment + PV of the second half of the post-discount payment

                                                                   = [First half of the post-discount payment × PVIF_{(r%, n)}]+ [Second half of the post-discount payment × PVIF_{(r%, n)}]

                                                                   = [$1,425,000 × PVIF_{(1%, 1)}]+ [$1,425,000 × PVIF_{(1%, 2)}]

                                                                   = [$1,425,000 × {1 / (1 + r)ⁿ}]+ [$1,425,000 × {1 / (1 + r)ⁿ}]

                                                                   = [$1,425,000 × {1 / (1 + 0.01)¹}]+ [$1,425,000 × {1 / (1 + 0.01)²}]

                                                                   = [$1,425,000 × 0.990099]+ [$1,425,000 × 0.980296]

                                                                   = $1,410,891.07 + $1,396,921.8

                                                                   = $2,807,812.87

Working notes-

Post-discount payment = List price × (1 – Discount rate)

                                     = $3,000,000 × (1 – 0.05)

                                     = $3,000,000 × 0.95

                                     = $2,850,000

Half of the post-discount payment = $2,850,000 / 2

                                                        = $1,425,000

Since, present value of cash outflows for offer 1 is less than the offer 2, so offer 1 should be selected.