4 years ago you bought a mobile phone on a 5-year contract which cost you $0 up

Question

4 years ago you bought a mobile phone on a 5-year contract which cost you $0 up front and requires monthly payments of $67 at the end of each month. Today your friend Ruby Ryan tells you she just bought a similar phone from another company for $115 up front and payments of only $53 at the end of each month. Furthermore, on the new plan, she can continue to pay the same $115 every 5 years to get a new handset.

(a) If your friend stays on the new plan for ever, and continues to buy a new handset every 5 years, what is the NPV of her decision to sign up? Both you and Ruby have a discount rate of 1.03% per month.

(b) You are wondering whether to break your contract and switch to the new provider to get the lower monthly rate. Your current provider has a break clause which means you have to pay a fee of $480 to terminate the contract today. Meanwhile the new phone company is so keen to attract new business they are offering financial incentives for customers from other providers. They are willing to pay you an amount today towards your costs of breaking your old contract if you sign up for 5 years. You would also have to bring your own handset initially (which the old company will unlock as part of the break fee) but then every 5 years you can pay the $115 to get a new handset. If you don't switch now, your contract expires in 1 year and you can take up the fresh offer at that date like Ruby has today. How much would the incentive need to be for it to be worthwhile for you to break the old contract today? Assume used mobile phones have no salvage value.

Explanation / Answer

a. Ruby is effectively paying $53 every month and $115 once every 5 years. We need to calculate the NPV of both these separately and sum them up.

NPV of the monthly payments = 53 / 1.03% = 5145.63

Discount rate for 5 years (60 months) = (1+1.03%)^60 - 1 = 84.94%

So NPV of the $115 once every 5 years = 115 / 84.94% + 115 (to account for the $115 that Ruby paid just now) = 250.40

So Total NPV = 5145.63 + 250.40 = 5396.03

Answer: NPV = 5396.03

b. If you decide NOT to break the contract, NPV of that decision will be 5396.03 one year down the line (same as Ruby) + NPV of the 12 payments made this year to the existing phone company

So NPV of deciding NOT to break the contract = 5396.03 / (1+1.03%)^12 + 67 * (1-1/(1+1.03%)^12) / 1.03% = 5,524.33

Let the financial incentive be X.

NPV of deciding to break the contract = 5396.03 (same as Ruby) - 480 (payment to existing phone company) + 115 (as the first payment of 115 is not required as you can bring your old phone) + X

So NPV of deciding to break the contract = 5031.03 + X

For both options to be equally attractive, NPV of deciding NOT to break the contract = NPV of deciding to break the contract

So 5,524.33 = 5031.03 + X

Solving, we get X = financial incentive = 493.30

Answer: Financial incentive = $493.30

Hope this helped ! Let me know in case of any queries.

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.