Chartered Financial Analyst Level 2

Explanation

To determine whether the rate implicit on the lease (RIIL) is lower, the same, or higher than the bank loan rate of 9.68%, we need to calculate the RIIL and compare it.

Given Information:

• Asset cost: GBP 80 million
• Bank loan rate: 9.68%
• Lease term: 10 years
• Annual lease payments: GBP 12 million (beginning of each year)
• Residual value: GBP 5 million (end of Year 10)
• Lessor's direct costs: GBP 2 million (at inception)

Calculating RIIL:

The rate implicit on the lease is the discount rate that makes the present value of lease payments plus the present value of the residual value equal to the fair value of the asset minus any lessor's direct costs.

Equation for RIIL: $\text{Fair Value} - \text{Lessor's Direct Costs} = \text{PV(Lease Payments)} + \text{PV(Residual Value)}$ $80,000,000 - 2,000,000 = \text{PV(12,000,000 annuity due)} + \text{PV(5,000,000)}$ $78,000,000 = 12,000,000 \times \left[ \frac{1 - (1+r)^{-10}}{r} \right] \times (1+r) + \frac{5,000,000}{(1+r)^{10}}$

Solving for r (RIIL): Using trial and error or financial calculator:

• At r = 9.68% (bank loan rate):
  • PV of lease payments (annuity due): 12,000,000 × [(1 - 1.0968^-10)/0.0968] × 1.0968 = 12,000,000 × 6.596 × 1.0968 = 86,800,000
  • PV of residual: 5,000,000 / 1.0968^10 = 5,000,000 / 2.525 = 1,980,000
  • Total PV = 86,800,000 + 1,980,000 = 88,780,000 > 78,000,000

Since the present value at 9.68% is higher than the target value of 78,000,000, we need a higher discount rate to reduce the present value. This means the RIIL must be lower than 9.68%.

Conclusion: The rate implicit on the lease is lower than the bank loan rate of 9.68%.